\displaystyle \textbf{Question 1. }\text{A man invests Rs. }8800\text{ in buying shares of a company of face value} \\ \text{Rs. }100\text{ each at a premium of }10\%.\text{ If he earns Rs. }1200\text{ as dividend at the end of} \\ \text{the year, find:}
\displaystyle \text{(i) The number of shares purchased.}
\displaystyle \text{(ii) The dividend percentage per share. [ICSE 2001]}
\displaystyle \text{Answer:}
\displaystyle \text{Face value of each share}=\text{Rs. }100
\displaystyle \text{Market price}=100+10\%\text{ of }100=\text{Rs. }110
\displaystyle \text{Number of shares}=\frac{8800}{110}=80
\displaystyle \text{Dividend received}=\text{Rs. }1200
\displaystyle \text{Let the dividend be }x\%\text{ per share.}
\displaystyle 80\times100\times\frac{x}{100}=1200
\displaystyle 80x=1200
\displaystyle x=15\%
\displaystyle \text{Hence, (i) the number of shares is }80
\displaystyle \text{and (ii) the dividend is }15\%\text{ per share.}
\\

\displaystyle \textbf{Question 2. }\text{A man invests Rs. }1680\text{ in buying shares of nominal value Rs. }24\text{ and} \\ \text{selling at }12\%\text{ premium. The dividend on the shares is }15\%\text{ per annum.} \\ \text{Calculate:}
\displaystyle \text{(i) The number of shares he buys.}
\displaystyle \text{(ii) The dividend he receives. [ICSE 1999]}
\displaystyle \text{Answer:}
\displaystyle \text{Face value of each share}=\text{Rs. }24
\displaystyle \text{Market price}=24+12\%\text{ of }24=24+2.88=\text{Rs. }26.88
\displaystyle \text{Number of shares}=\frac{1680}{26.88}=62.5
\displaystyle \text{Dividend per share}=15\%\text{ of Rs. }24=\text{Rs. }3.60
\displaystyle \text{Total dividend}=62.5\times3.60=\text{Rs. }225
\displaystyle \text{Hence, (i) the number of shares is }62.5
\displaystyle \text{and (ii) the dividend received is Rs. }225.
\\

\displaystyle \textbf{Question 3. }\text{By investing Rs. }7500\text{ in a company paying }10\%\text{ dividend, an annual} \\ \text{income of Rs. }500\text{ is received. What price is paid for each Rs. }100\text{ share?} \\ \text{[1990]}
\displaystyle \text{Answer:}
\displaystyle \text{Let the market price of each share be Rs. }x.
\displaystyle \text{Number of shares purchased}=\frac{7500}{x}
\displaystyle \text{Dividend per share}=10\%\text{ of Rs. }100=\text{Rs. }10
\displaystyle \frac{7500}{x}\times10=500
\displaystyle \frac{75000}{x}=500
\displaystyle 75000=500x
\displaystyle x=150
\displaystyle \text{Hence, the price paid for each share is Rs. }150.
\\

\displaystyle \textbf{Question 4. }\text{A man invests Rs. }20020\text{ in buying shares of N.V. Rs. }26\text{ at }10\% \\ \text{premium. The dividend on the shares is }15\%\text{ per annum. Calculate:}
\displaystyle \text{(i) The number of shares he buys.}
\displaystyle \text{(ii) The dividend he receives annually.}
\displaystyle \text{(iii) The rate of interest he gets on his money. [ICSE 2012]}
\displaystyle \text{Answer:}
\displaystyle \text{Market value of each share}=26+10\%\text{ of }26=\text{Rs. }28.60
\displaystyle \text{Number of shares}=\frac{20020}{28.60}=700
\displaystyle \text{Annual dividend}=700\times26\times\frac{15}{100}=\text{Rs. }2730
\displaystyle \text{Rate of interest}=\frac{2730}{20020}\times100=13.64\%
\displaystyle \text{Hence, he buys }700\text{ shares, receives Rs. }2730
\displaystyle \text{as annual dividend and gets }13.64\%\text{ interest on his money.}
\\

\displaystyle \textbf{Question 5. }\text{A man invested Rs. }45000\text{ in }15\%\text{ Rs. }100\text{ shares quoted at Rs. }125. \\ \text{When the M.V. of these shares rose to Rs. }140,\text{ he sold some shares, just enough} \\ \text{to raise Rs. }8400.\text{ Calculate:}
\displaystyle \text{(i) The number of shares he still holds.}
\displaystyle \text{(ii) The dividend due to him on these remaining shares. [ICSE 2004]}
\displaystyle \text{Answer:}
\displaystyle \text{Nominal value of each share}=\text{Rs. }100
\displaystyle \text{Market value of each share}=\text{Rs. }125
\displaystyle \text{Number of shares bought}=\frac{45000}{125}=360
\displaystyle \text{Selling price of each share}=\text{Rs. }140
\displaystyle \text{Number of shares sold}=\frac{8400}{140}=60
\displaystyle \text{Number of shares left}=360-60=300
\displaystyle \text{Dividend on remaining shares}=300\times100\times\frac{15}{100}
\displaystyle =\text{Rs. }4500
\displaystyle \text{Hence, he still holds }300\text{ shares and receives Rs. }4500\text{ as dividend.}
\\

\displaystyle \textbf{Question 6. }\text{Vivek invests Rs. }4500\text{ in }8\%\text{ Rs. }10\text{ shares at Rs. }15. \\ \text{He sells the shares when the price rises to Rs. }30\text{ and invests the proceeds} \\ \text{in }12\%\text{ Rs. }100\text{ shares at Rs. }125.\text{ Calculate:}
\displaystyle \text{(i) The sale proceeds.}
\displaystyle \text{(ii) The number of Rs. }125\text{ shares he buys.}
\displaystyle \text{(iii) The change in his annual income from dividend. [ICSE 2010]}
\displaystyle \text{Answer:}
\displaystyle \text{First investment:}
\displaystyle \text{Market value of each share}=\text{Rs. }15
\displaystyle \text{Number of shares bought}=\frac{4500}{15}=300
\displaystyle \text{Sale proceeds}=300\times30=\text{Rs. }9000
\displaystyle \text{Annual dividend from first investment}=300\times10\times\frac{8}{100}
\displaystyle =\text{Rs. }240
\displaystyle \text{Second investment:}
\displaystyle \text{Market value of each share}=\text{Rs. }125
\displaystyle \text{Number of shares bought}=\frac{9000}{125}=72
\displaystyle \text{Annual dividend from second investment}=72\times100\times\frac{12}{100}
\displaystyle =\text{Rs. }864
\displaystyle \text{Change in annual income}=864-240=\text{Rs. }624
\displaystyle \text{Hence, the sale proceeds are Rs. }9000,\text{ he buys }72\text{ shares,}
\displaystyle \text{and his annual income increases by Rs. }624.
\\

\displaystyle \textbf{Question 7. }\text{Mr. Parekh invested Rs. }52000\text{ on Rs. }100\text{ shares at a discount of} \\ \text{Rs. }20\text{ paying }8\%\text{ dividend. At the end of one year he sells the shares at} \\ \text{a premium of Rs. }20.\text{ Find:}
\displaystyle \text{(i) The annual dividend.}
\displaystyle \text{(ii) The profit earned including his dividend. [ICSE 2011]}
\displaystyle \text{Answer:}
\displaystyle \text{Face value of each share}=\text{Rs. }100
\displaystyle \text{Market price}=100-20=\text{Rs. }80
\displaystyle \text{Number of shares}=\frac{52000}{80}=650
\displaystyle \text{Annual dividend}=650\times100\times\frac{8}{100}=\text{Rs. }5200
\displaystyle \text{Selling price per share}=100+20=\text{Rs. }120
\displaystyle \text{Sale proceeds}=650\times120=\text{Rs. }78000
\displaystyle \text{Capital profit}=78000-52000=\text{Rs. }26000
\displaystyle \text{Total profit including dividend}=26000+5200=\text{Rs. }31200
\displaystyle \text{Hence, (i) the annual dividend is Rs. }5200
\displaystyle \text{and (ii) the total profit is Rs. }31200.
\\

\displaystyle \textbf{Question 8. }\text{Salman buys }50\text{ shares of face value Rs. }100\text{ available at Rs. }132. \\ \text{Find: (i) His investment. (ii) His annual income if the dividend is }7.5\%. \\ \text{(iii) If he wants to increase his annual income by Rs. }150,\text{ how many extra} \\ \text{shares should he buy? [ICSE 2013]}
\displaystyle \text{Answer:}
\displaystyle \text{Face value of each share}=\text{Rs. }100
\displaystyle \text{Market price of each share}=\text{Rs. }132
\displaystyle \text{Number of shares}=50
\displaystyle \text{Investment}=50\times132=\text{Rs. }6600
\displaystyle \text{Annual dividend}=50\times100\times\frac{7.5}{100}=\text{Rs. }375
\displaystyle \text{Dividend on one share}=100\times\frac{7.5}{100}=\text{Rs. }7.50
\displaystyle \text{Extra shares required}=\frac{150}{7.5}=20
\displaystyle \text{Hence, (i) the investment is Rs. }6600,\text{ (ii) the annual}
\displaystyle \text{income is Rs. }375\text{ and (iii) he should buy }20\text{ more shares.}
\\

\displaystyle \textbf{Question 9. }\text{Salman invests a sum of money in Rs. }50\text{ shares paying }15\%\text{ dividend} \\ \text{quoted at }20\%\text{ premium. If his annual dividend is Rs. }600,\text{ calculate:}
\displaystyle \text{(i) The number of shares he bought.}
\displaystyle \text{(ii) His total investment.}
\displaystyle \text{(iii) The rate of return on his investment. [ICSE 2004]}
\displaystyle \text{Answer:}
\displaystyle \text{Face value of each share}=\text{Rs. }50
\displaystyle \text{Market price}=50+20\%\text{ of }50=\text{Rs. }60
\displaystyle \text{Dividend per share}=50\times\frac{15}{100}=\text{Rs. }7.50
\displaystyle \text{Number of shares}=\frac{600}{7.5}=80
\displaystyle \text{Total investment}=80\times60=\text{Rs. }4800
\displaystyle \text{Rate of return}=\frac{600}{4800}\times100=12.5\%
\displaystyle \text{Hence, (i) the number of shares is }80,
\displaystyle \text{(ii) the investment is Rs. }4800\text{ and (iii) the rate of return is }12.5\%.
\\

\displaystyle \textbf{Question 10. }\text{The sum invested to purchase }15\text{ shares of a company of nominal} \\ \text{value Rs. }75\text{ available at a discount of }20\%\text{ is: [ICSE 2024]}
\displaystyle \text{(a) Rs. }60\qquad\text{(b) Rs. }90\qquad\text{(c) Rs. }1350\qquad\text{(d) Rs. }900
\displaystyle \text{Answer:}
\displaystyle \text{(d) Given, number of shares}=15
\displaystyle \text{Face value of each share}=\text{Rs. }75
\displaystyle \text{Market price}=75\left(1-\frac{20}{100}\right)=75\times\frac{4}{5}=\text{Rs. }60
\displaystyle \text{Investment}=15\times60=\text{Rs. }900
\displaystyle \text{Hence, the required sum invested is Rs. }900.
\\

 

\displaystyle \textbf{Question 11. }\text{Mr. Gupta invested Rs. }3300\text{ in buying Rs. }100\text{ shares of a company} \\ \text{at }10\%\text{ premium. The dividend declared by the company is }12\%.\text{ Find:}
\displaystyle \text{(i) The number of shares purchased by him.}
\displaystyle \text{(ii) His annual dividend. [ICSE 2024]}
\displaystyle \text{Answer:}
\displaystyle \text{Amount invested}=\text{Rs. }3300
\displaystyle \text{Face value of each share}=\text{Rs. }100
\displaystyle \text{Market price}=100+10\%\text{ of }100=\text{Rs. }110
\displaystyle \text{Number of shares}=\frac{3300}{110}=30
\displaystyle \text{Annual dividend}=30\times100\times\frac{12}{100}
\displaystyle =\text{Rs. }360
\displaystyle \text{Hence, (i) the number of shares purchased is }30
\displaystyle \text{and (ii) the annual dividend is Rs. }360.
\\

\displaystyle \textbf{Question 12. }\text{Mr. Sharma receives an annual income of Rs. }900\text{ by investing in} \\ \text{Rs. }50\text{ shares selling at Rs. }80.\text{ If the dividend declared is }20\%,\text{ find:}
\displaystyle \text{(i) The amount invested by Mr. Sharma.}
\displaystyle \text{(ii) The percentage return on his investment. [ICSE 2020]}
\displaystyle \text{Answer:}
\displaystyle \text{Annual dividend received}=\text{Rs. }900
\displaystyle \text{Face value of each share}=\text{Rs. }50,\qquad \text{Market price}=\text{Rs. }80
\displaystyle \text{Dividend per share}=50\times\frac{20}{100}=\text{Rs. }10
\displaystyle \text{Number of shares}=\frac{900}{10}=90
\displaystyle \text{(i) Amount invested}=90\times80=\text{Rs. }7200
\displaystyle \text{(ii) Percentage return}=\frac{900}{7200}\times100=12.5\%
\displaystyle \text{Hence, (i) the amount invested is Rs. }7200
\displaystyle \text{and (ii) the percentage return is }12.5\%.
\\

\displaystyle \textbf{Question 13. }\text{A man invests Rs. }22500\text{ in Rs. }50\text{ shares available at }10\%\text{ discount.} \\ \text{If the dividend paid by the company is }12\%,\text{ calculate:}
\displaystyle \text{(i) The number of shares purchased.}
\displaystyle \text{(ii) The annual dividend received.}
\displaystyle \text{(iii) The rate of return on his investment, correct to the nearest whole number.} \\ \text{[ICSE 2018]}
\displaystyle \text{Answer:}
\displaystyle \text{Face value of each share}=\text{Rs. }50
\displaystyle \text{Market price}=50-10\%\text{ of }50=\text{Rs. }45
\displaystyle \text{Amount invested}=\text{Rs. }22500
\displaystyle \text{(i) Number of shares}=\frac{22500}{45}=500
\displaystyle \text{(ii) Annual dividend}=500\times50\times\frac{12}{100}
\displaystyle =\text{Rs. }3000
\displaystyle \text{(iii) Rate of return}=\frac{3000}{22500}\times100=13.33\%
\displaystyle \approx13\%\text{ (nearest whole number)}
\displaystyle \text{Hence, (i) the number of shares is }500,\text{ (ii) the annual dividend is}
\displaystyle \text{Rs. }3000\text{ and (iii) the rate of return is }13\%.
\\

\displaystyle \textbf{Question 14. }\text{How much should a man invest in Rs. }50\text{ shares selling at Rs. }60 \\ \text{to obtain an income of Rs. }450,\text{ if the rate of dividend declared is }10\%? \\ \text{Also, find his yield percent, to the nearest whole number. [ICSE 2017]}
\displaystyle \text{Answer:}
\displaystyle \text{Dividend per share}=50\times\frac{10}{100}=\text{Rs. }5
\displaystyle \text{Number of shares}=\frac{450}{5}=90
\displaystyle \text{Market price of each share}=\text{Rs. }60
\displaystyle \text{Total investment}=90\times60=\text{Rs. }5400
\displaystyle \text{Yield}=\frac{450}{5400}\times100=8.33\%
\displaystyle \approx8\%\text{ (nearest whole number)}
\displaystyle \text{Hence, the required investment is Rs. }5400
\displaystyle \text{and the yield is }8\%.
\\

\displaystyle \textbf{Question 15. }\text{Ashok invested Rs. }26400\text{ on }12\%\text{ Rs. }25\text{ shares of a company.} \\ \text{If he receives a dividend of Rs. }2475,\text{ find:}
\displaystyle \text{(i) The number of shares he bought.}
\displaystyle \text{(ii) The market value of each share. [ICSE 2016]}
\displaystyle \text{Answer:}
\displaystyle \text{Annual dividend received}=\text{Rs. }2475
\displaystyle \text{Dividend per share}=25\times\frac{12}{100}=\text{Rs. }3
\displaystyle \text{(i) Number of shares}=\frac{2475}{3}=825
\displaystyle \text{(ii) Market price of each share}=\frac{26400}{825}=\text{Rs. }32
\displaystyle \text{Hence, (i) the number of shares purchased is }825
\displaystyle \text{and (ii) the market value of each share is Rs. }32.
\\

\displaystyle \textbf{Question 16. }\text{Salman invests a sum of money in Rs. }50\text{ shares paying }15\%\text{ dividend} \\ \text{quoted at }20\%\text{ premium. If his annual dividend is Rs. }600,\text{ calculate:}
\displaystyle \text{(i) The number of shares he bought.}
\displaystyle \text{(ii) His total investment.}
\displaystyle \text{(iii) The rate of return on his investment. [ICSE 2014]}
\displaystyle \text{Answer:}
\displaystyle \text{Face value of each share}=\text{Rs. }50
\displaystyle \text{Dividend per share}=50\times\frac{15}{100}=\text{Rs. }7.50
\displaystyle \text{Annual dividend received}=\text{Rs. }600
\displaystyle \text{(i) Number of shares}=\frac{600}{7.50}=80
\displaystyle \text{Premium per share}=20\%\text{ of }50=\text{Rs. }10
\displaystyle \text{Market price of each share}=50+10=\text{Rs. }60
\displaystyle \text{(ii) Total investment}=80\times60=\text{Rs. }4800
\displaystyle \text{(iii) Rate of return}=\frac{600}{4800}\times100=12.5\%
\displaystyle \text{Hence, (i) the number of shares is }80,\text{ (ii) the investment is}
\displaystyle \text{Rs. }4800\text{ and (iii) the rate of return is }12.5\%.
\\

\displaystyle \textbf{Question 17. }\text{A man invests Rs. }9600\text{ in Rs. }100\text{ shares at Rs. }80.\text{ If the company pays} \\ \text{an }18\%\text{ dividend, find:}
\displaystyle \text{(i) The number of shares he buys.}
\displaystyle \text{(ii) His total dividend.}
\displaystyle \text{(iii) His percentage return on the shares. [ICSE 2012]}
\displaystyle \text{Answer:}
\displaystyle \text{Amount invested}=\text{Rs. }9600
\displaystyle \text{Face value of each share}=\text{Rs. }100,\qquad \text{Market price}=\text{Rs. }80
\displaystyle \text{Dividend rate}=18\%
\displaystyle \text{(i) Number of shares}=\frac{9600}{80}=120
\displaystyle \text{(ii) Total dividend}=120\times100\times\frac{18}{100}=\text{Rs. }2160
\displaystyle \text{(iii) Percentage return}=\frac{2160}{9600}\times100=22.5\%
\displaystyle \text{Hence, (i) the number of shares is }120,\text{ (ii) the dividend is}
\displaystyle \text{Rs. }2160\text{ and (iii) the percentage return is }22.5\%.
\\

\displaystyle \textbf{Question 18. }\text{Mr. Prakash invested Rs. }52000\text{ in Rs. }100\text{ shares at a discount of} \\ \text{Rs. }20\text{ paying }8\%\text{ dividend. At the end of one year he sells the shares at} \\ \text{a premium of Rs. }20.\text{ Find:}
\displaystyle \text{(i) The annual dividend.}
\displaystyle \text{(ii) The profit earned including his dividend. [ICSE 2011]}
\displaystyle \text{Answer:}
\displaystyle \text{Amount invested}=\text{Rs. }52000
\displaystyle \text{Face value of each share}=\text{Rs. }100
\displaystyle \text{Market price}=100-20=\text{Rs. }80,\qquad \text{Dividend rate}=8\%
\displaystyle \text{Number of shares}=\frac{52000}{80}=650
\displaystyle \text{(i) Annual dividend}=650\times100\times\frac{8}{100}=\text{Rs. }5200
\displaystyle \text{Selling price per share}=100+20=\text{Rs. }120
\displaystyle \text{Sale proceeds}=650\times120=\text{Rs. }78000
\displaystyle \text{(ii) Total profit including dividend}=(78000-52000)+5200
\displaystyle =26000+5200=\text{Rs. }31200
\displaystyle \text{Hence, (i) the annual dividend is Rs. }5200
\displaystyle \text{and (ii) the total profit including dividend is Rs. }31200.
\\

\displaystyle \textbf{Question 19. }\text{Amit Kumar invests Rs. }36000\text{ in buying Rs. }100\text{ shares at} \\ \text{a premium of Rs. }20.\text{ The dividend is }15\%\text{ per annum. Find:}
\displaystyle \text{(i) The number of shares he buys.}
\displaystyle \text{(ii) His yearly dividend.}
\displaystyle \text{(iii) The percentage return on his investment. Give your answer} \\ \text{correct to the nearest whole number. [ICSE 2009]}
\displaystyle \text{Answer:}
\displaystyle \text{Face value of each share}=\text{Rs. }100
\displaystyle \text{Market price}=100+20=\text{Rs. }120
\displaystyle \text{Amount invested}=\text{Rs. }36000,\qquad \text{Dividend rate}=15\%
\displaystyle \text{(i) Number of shares}=\frac{36000}{120}=300
\displaystyle \text{Dividend per share}=100\times\frac{15}{100}=\text{Rs. }15
\displaystyle \text{(ii) Annual dividend}=300\times15=\text{Rs. }4500
\displaystyle \text{(iii) Percentage return}=\frac{4500}{36000}\times100=12.5\%
\displaystyle \approx13\%\text{ (nearest whole number)}
\displaystyle \text{Hence, (i) the number of shares is }300,\text{ (ii) the yearly dividend is}
\displaystyle \text{Rs. }4500\text{ and (iii) the percentage return is }13\%.
\\

\displaystyle \textbf{Question 20. }\text{Ajay owns }560\text{ shares of a company. The face value of each share is} \\ \text{Rs. }25.\text{ The company declares a dividend of }9\%.\text{ Calculate:}
\displaystyle \text{(i) The dividend that Ajay will get.}
\displaystyle \text{(ii) The rate of interest on his investment, if Ajay had paid Rs. }30 \\ \text{for each share. [ICSE 2007]}
\displaystyle \text{Answer:}
\displaystyle \text{Number of shares}=560,\qquad \text{Face value of each share}=\text{Rs. }25
\displaystyle \text{Dividend rate}=9\%
\displaystyle \text{Dividend per share}=25\times\frac{9}{100}=\text{Rs. }\frac{9}{4}
\displaystyle \text{(i) Total dividend}=560\times\frac{9}{4}=\text{Rs. }1260
\displaystyle \text{Amount invested}=560\times30=\text{Rs. }16800
\displaystyle \text{(ii) Rate of return}=\frac{1260}{16800}\times100=7.5\%
\displaystyle \text{Hence, (i) the dividend received is Rs. }1260
\displaystyle \text{and (ii) the rate of return is }7.5\%.
\\

\displaystyle \textbf{Question 21. }\text{Mr. Tiwari invested Rs. }29040\text{ in }15\%\text{ Rs. }100\text{ shares quoted} \\ \text{at a premium of }20\%.\text{ Calculate:}
\displaystyle \text{(i) The number of shares bought by Mr. Tiwari.}
\displaystyle \text{(ii) Mr. Tiwari's income from the investment.}
\displaystyle \text{(iii) The percentage return on his investment. [ICSE 2005]}
\displaystyle \text{Answer:}
\displaystyle \text{Amount invested}=\text{Rs. }29040,\qquad \text{Face value of each share}=\text{Rs. }100
\displaystyle \text{Dividend rate}=15\%,\qquad \text{Premium}=20\%
\displaystyle \text{(i) Market price}=100+20\%\text{ of }100=\text{Rs. }120
\displaystyle \text{Number of shares}=\frac{29040}{120}=242
\displaystyle \text{(ii) Annual income}=242\times100\times\frac{15}{100}=\text{Rs. }3630
\displaystyle \text{(iii) Percentage return}=\frac{3630}{29040}\times100=12.5\%
\displaystyle \text{Hence, (i) the number of shares is }242,\text{ (ii) the annual income is}
\displaystyle \text{Rs. }3630\text{ and (iii) the percentage return is }12.5\%.
\\

\displaystyle \textbf{Question 22. }\text{A man invests Rs. }8800\text{ in buying shares of face value} \\ \text{Rs. }100\text{ each at a premium of }10\%.\text{ If he earns Rs. }1200\text{ as dividend at the end of} \\ \text{the year, find:}
\displaystyle \text{(i) The number of shares he has in the company.}
\displaystyle \text{(ii) The dividend percentage per share. [ICSE 2001]}
\displaystyle \text{Answer:}
\displaystyle \text{Amount invested}=\text{Rs. }8800,\qquad \text{Face value of each share}=\text{Rs. }100
\displaystyle \text{Market price}=100+10\%\text{ of }100=\text{Rs. }110
\displaystyle \text{(i) Number of shares}=\frac{8800}{110}=80
\displaystyle \text{(ii) Let the dividend rate be }x\%
\displaystyle 80\times100\times\frac{x}{100}=1200
\displaystyle 80x=1200
\displaystyle x=15\%
\displaystyle \text{Hence, (i) the number of shares is }80
\displaystyle \text{and (ii) the dividend percentage is }15\%.
\\

\displaystyle \textbf{Question 23. }\text{A man bought }200\text{ shares each of face value Rs. }10\text{ at Rs. }12\text{ per share.} \\ \text{At the end of the year, the company declares a dividend of }15\%.\text{ Calculate:}
\displaystyle \text{(i) The amount of money invested by the man.}
\displaystyle \text{(ii) The amount of dividend he received.}
\displaystyle \text{(iii) The percentage return on his outlay. [ICSE 2017]}
\displaystyle \text{Answer:}
\displaystyle \text{Face value of each share}=\text{Rs. }10,\qquad \text{Market price}=\text{Rs. }12
\displaystyle \text{Number of shares}=200,\qquad \text{Dividend rate}=15\%
\displaystyle \text{(i) Amount invested}=200\times12=\text{Rs. }2400
\displaystyle \text{(ii) Dividend received}=200\times10\times\frac{15}{100}=\text{Rs. }300
\displaystyle \text{(iii) Percentage return}=\frac{300}{2400}\times100=12.5\%
\displaystyle \text{Hence, (i) the amount invested is Rs. }2400,\text{ (ii) the dividend is}
\displaystyle \text{Rs. }300\text{ and (iii) the percentage return is }12.5\%.
\\

\displaystyle \textbf{Question 24. }\text{Rohit invested Rs. }9600\text{ in Rs. }100\text{ shares at Rs. }20\text{ premium} \\ \text{paying }8\%\text{ dividend. Rohit sold the shares when the price rose to Rs. }160. \\ \text{He invested the proceeds, excluding dividend, in }10\%\text{ Rs. }50\text{ shares at Rs. }40. \\ \text{Find:}
\displaystyle \text{(i) Original number of shares.}
\displaystyle \text{(ii) Sale proceeds.}
\displaystyle \text{(iii) New number of shares.}
\displaystyle \text{(iv) Change in the two dividends. [ICSE 2015]}
\displaystyle \text{Answer:}
\displaystyle \text{Market price of original share}=100+20=\text{Rs. }120
\displaystyle \text{(i) Original number of shares}=\frac{9600}{120}=80
\displaystyle \text{(ii) Sale proceeds}=80\times160=\text{Rs. }12800
\displaystyle \text{Market price of new share}=\text{Rs. }40
\displaystyle \text{(iii) New number of shares}=\frac{12800}{40}=320
\displaystyle \text{Original dividend}=80\times100\times\frac{8}{100}=\text{Rs. }640
\displaystyle \text{New dividend}=320\times50\times\frac{10}{100}=\text{Rs. }1600
\displaystyle \text{(iv) Change in dividend}=1600-640=\text{Rs. }960
\displaystyle \text{Hence, the annual dividend increases by Rs. }960.
\\

\displaystyle \textbf{Question 25. }\text{Salman buys }50\text{ shares of face value Rs. }100\text{ available at Rs. }132. \\ \text{Find:}
\displaystyle \text{(i) His investment.}
\displaystyle \text{(ii) His annual income, if the dividend is }7.5\%.
\displaystyle \text{(iii) The number of extra shares he should buy to increase his annual income} \\ \text{by Rs. }150.\text{ [ICSE 2013]}
\displaystyle \text{Answer:}
\displaystyle \text{Number of shares}=50,\qquad \text{Face value of each share}=\text{Rs. }100
\displaystyle \text{Market price of each share}=\text{Rs. }132
\displaystyle \text{(i) Investment}=50\times132=\text{Rs. }6600
\displaystyle \text{Dividend per share}=100\times\frac{7.5}{100}=\text{Rs. }7.50
\displaystyle \text{(ii) Annual income}=50\times7.5=\text{Rs. }375
\displaystyle \text{Extra dividend required}=\text{Rs. }150
\displaystyle \text{(iii) Extra shares}=\frac{150}{7.5}=20
\displaystyle \text{Hence, (i) the investment is Rs. }6600,\text{ (ii) the annual income is}
\displaystyle \text{Rs. }375\text{ and (iii) he should buy }20\text{ extra shares.}
\\

\displaystyle \textbf{Question 26. }\text{Vivek invests Rs. }4500\text{ in }8\%\text{ Rs. }10\text{ shares at Rs. }15. \\ \text{He sells the shares when the price rises to Rs. }30\text{ and invests the proceeds in} \\ 12\%\text{ Rs. }100\text{ shares at Rs. }125.\text{ Calculate:}
\displaystyle \text{(i) The sale proceeds.}
\displaystyle \text{(ii) The number of Rs. }125\text{ shares he buys.}
\displaystyle \text{(iii) The change in his annual income from dividend. [ICSE 2010]}
\displaystyle \text{Answer:}
\displaystyle \text{Amount invested}=\text{Rs. }4500,\qquad \text{Market price of each share}=\text{Rs. }15
\displaystyle \text{Number of shares bought}=\frac{4500}{15}=300
\displaystyle \text{(i) Sale proceeds}=300\times30=\text{Rs. }9000
\displaystyle \text{Market price of new share}=\text{Rs. }125
\displaystyle \text{(ii) Number of new shares}=\frac{9000}{125}=72
\displaystyle \text{Original dividend}=300\times10\times\frac{8}{100}=\text{Rs. }240
\displaystyle \text{New dividend}=72\times100\times\frac{12}{100}=\text{Rs. }864
\displaystyle \text{(iii) Change in annual income}=864-240=\text{Rs. }624
\displaystyle \text{Hence, (i) the sale proceeds are Rs. }9000,\text{ (ii) the number of}
\displaystyle \text{new shares is }72\text{ and (iii) the increase in annual income is Rs. }624.
\\

\displaystyle \textbf{Question 27. }\text{A company with }4000\text{ shares of nominal value Rs. }110\text{ each} \\ \text{declares an annual dividend of }15\%.\text{ Calculate:}
\displaystyle \text{(i) The total amount of dividend paid by the company.}
\displaystyle \text{(ii) The annual income of Shahrukh, who holds }88\text{ shares in the company.}
\displaystyle \text{(iii) If he received only }10\%\text{ on his investment, find the price} \\ \text{Shahrukh paid for each share. [ICSE 2008]}
\displaystyle \text{Answer:}
\displaystyle \text{Number of shares}=4000,\qquad \text{Face value of each share}=\text{Rs. }110
\displaystyle \text{Dividend rate}=15\%
\displaystyle \text{Dividend per share}=110\times\frac{15}{100}=\text{Rs. }16.50
\displaystyle \text{(i) Total dividend}=4000\times16.50=\text{Rs. }66000
\displaystyle \text{(ii) Shahrukh's annual income}=88\times16.50=\text{Rs. }1452
\displaystyle \text{Let Shahrukh's total investment be Rs. }x
\displaystyle \text{Since the return is }10\%,\qquad \frac{10x}{100}=1452
\displaystyle x=\frac{1452\times100}{10}=\text{Rs. }14520
\displaystyle \text{(iii) Price paid per share}=\frac{14520}{88}=\text{Rs. }165
\displaystyle \text{Hence, (i) the total dividend paid is Rs. }66000,
\displaystyle \text{(ii) Shahrukh's annual income is Rs. }1452\text{ and (iii) he paid}
\displaystyle \text{Rs. }165\text{ for each share.}
\\

\displaystyle \textbf{Question 28. }\text{Mr. Ram Gopal invested Rs. }8000\text{ in }7\%\text{ Rs. }100\text{ shares at Rs. }80. \\ \text{After a year, he sold these shares at Rs. }75\text{ each and invested the proceeds} \\ \text{in }18\%\text{ Rs. }25\text{ shares at Rs. }41.\text{ Find:}
\displaystyle \text{(i) His dividend for the first year.}
\displaystyle \text{(ii) His annual income from the second investment.}
\displaystyle \text{(iii) The percentage increase in return on his original investment. [ICSE 2006]}
\displaystyle \text{Answer:}
\displaystyle \text{Number of shares bought}=\frac{8000}{80}=100
\displaystyle \text{(i) Dividend for first year}=100\times100\times\frac{7}{100}=\text{Rs. }700
\displaystyle \text{Sale proceeds}=100\times75=\text{Rs. }7500
\displaystyle \text{Total amount reinvested}=7500+700=\text{Rs. }8200
\displaystyle \text{Number of new shares bought}=\frac{8200}{41}=200
\displaystyle \text{(ii) Annual income from second investment}=200\times25\times\frac{18}{100}
\displaystyle =\text{Rs. }900
\displaystyle \text{Increase in annual income}=900-700=\text{Rs. }200
\displaystyle \text{(iii) Percentage increase}=\frac{200}{8000}\times100=2.5\%
\displaystyle \text{Hence, his first-year dividend is Rs. }700,\text{ his second annual income}
\displaystyle \text{is Rs. }900\text{ and the percentage increase is }2.5\%.
\\

\displaystyle \textbf{Question 29. }\text{A man invested Rs. }45000\text{ in }15\%\text{ Rs. }100\text{ shares quoted at} \\ \text{Rs. }125.\text{ When the market value of these shares rose to Rs. }140,\text{ he sold} \\ \text{some shares, just enough to raise Rs. }8400.\text{ Calculate:}
\displaystyle \text{(i) The number of shares he still holds.}
\displaystyle \text{(ii) The dividend due to him on these remaining shares. [ICSE 2004]}
\displaystyle \text{Answer:}
\displaystyle \text{Amount invested}=\text{Rs. }45000,\qquad \text{Face value of each share}=\text{Rs. }100
\displaystyle \text{Market price of each share}=\text{Rs. }125,\qquad \text{Dividend rate}=15\%
\displaystyle \text{Number of shares bought}=\frac{45000}{125}=360
\displaystyle \text{Shares sold}=\frac{8400}{140}=60
\displaystyle \text{(i) Shares still held}=360-60=300
\displaystyle \text{(ii) Dividend on remaining shares}=300\times100\times\frac{15}{100}
\displaystyle =\text{Rs. }4500
\displaystyle \text{Hence, (i) the number of shares still held is }300
\displaystyle \text{and (ii) the dividend due on these shares is Rs. }4500.
\\

\displaystyle \textbf{Question 30. }\text{A company with }10000\text{ shares of Rs. }100\text{ each, declares an annual dividend}
\displaystyle \text{of }5\%.\text{ Find:} \hspace{0.2cm}\text{[ICSE 1998]}
\displaystyle \text{(i) What is the total amount of dividend paid by company?}
\displaystyle \text{(ii) What would be the annual income of a man, who has }72\text{ shares in the company?}
\displaystyle \text{(iii) If he received only }4\%\text{ on his investment, find the price he had paid for each share.}
\displaystyle \text{Answer:}
\displaystyle \text{Dividend on one share}=5\%\text{ of }100=5
\displaystyle \text{Total dividend}=10000\times5=50000
\displaystyle \therefore \text{(i) Total dividend paid = Rs. }50000
\displaystyle \text{Annual income for }72\text{ shares}=72\times5=360
\displaystyle \therefore \text{(ii) Annual income = Rs. }360
\displaystyle \text{Let the price paid for each share be Rs. }x
\displaystyle \text{Investment}=72x
\displaystyle 4\%\text{ of }72x=360
\displaystyle \frac{4}{100}\times72x=360
\displaystyle x=\frac{360\times100}{4\times72}=125
\displaystyle \therefore \text{(iii) Price paid for each share = Rs. }125
\\

\displaystyle \textbf{Question 31. }\text{A man sold }400\text{ Rs. }20\text{ shares paying }5\%\text{ at Rs. }18\text{ and invested the proceeds}
\displaystyle \text{in Rs. }10\text{ shares paying }7\%\text{ at Rs. }12.\text{ How many Rs. }10\text{ shares did he buy}
\displaystyle \text{and what was the change of income?} \hspace{0.2cm}\text{[ICSE 1989]}
\displaystyle \text{Answer:}
\displaystyle \text{Amount obtained by selling shares}=400\times18=7200
\displaystyle \text{Number of new shares bought}=\frac{7200}{12}=600
\displaystyle \therefore \text{Number of Rs. }10\text{ shares bought}=600
\displaystyle \text{Old income}=400\times5\%\text{ of }20
\displaystyle =400\times\frac{5}{100}\times20=400
\displaystyle \text{New income}=600\times7\%\text{ of }10
\displaystyle =600\times\frac{7}{100}\times10=420
\displaystyle \text{Change in income}=420-400=20
\displaystyle \therefore \text{Income increases by Rs. }20
\\

\displaystyle \textbf{Question 32. }\text{A lady holds }1800\text{ hundred rupee shares of a company that pays }15\%\text{ dividend}
\displaystyle \text{annually. Calculate her annual dividend, if she had bought these shares at }40\%\text{ premium.}
\displaystyle \text{What percentage return would she have got on her investment? Give your answer to}
\displaystyle \text{nearest integer.} \hspace{0.2cm}\text{[ICSE 1997]}
\displaystyle \text{Answer:}
\displaystyle \text{Face value of each share}=\text{Rs. }100
\displaystyle \text{Dividend on one share}=15\%\text{ of }100=15
\displaystyle \text{Annual dividend}=1800\times15=27000
\displaystyle \therefore \text{Annual dividend = Rs. }27000
\displaystyle \text{Market value of each share}=100+40\%\text{ of }100=140
\displaystyle \text{Total investment}=1800\times140=252000
\displaystyle \text{Percentage return}=\frac{27000}{252000}\times100
\displaystyle =10.714\%
\displaystyle \approx 11\%
\displaystyle \therefore \text{Percentage return on investment}=11\%
\\

\displaystyle \textbf{Question 33. }\text{By purchasing Rs. }25\text{ shares for Rs. }40\text{ each a man gets }4\text{ per cent profit on}
\displaystyle \text{his investment. What rate per cent is the company paying? What is his dividend}
\displaystyle \text{if he buys }60\text{ shares?} \hspace{0.2cm}\text{[ICSE 1987]}
\displaystyle \text{Answer:}
\displaystyle \text{Investment on one share}=\text{Rs. }40
\displaystyle \text{Income on one share}=4\%\text{ of }40
\displaystyle =\frac{4}{100}\times40=1.60
\displaystyle \text{Let the company pay dividend at }x\%
\displaystyle x\%\text{ of }25=1.60
\displaystyle \frac{x}{100}\times25=1.60
\displaystyle x=\frac{1.60\times100}{25}=6.4
\displaystyle \therefore \text{Rate of dividend}=6.4\%
\displaystyle \text{Dividend on }60\text{ shares}=60\times1.60=96
\displaystyle \therefore \text{Dividend on }60\text{ shares = Rs. }96
\\

\displaystyle \textbf{Question 34. }\text{Mr. Parekh invested Rs. }52000\text{ on Rs. }100\text{ shares at a discount of Rs. }20\text{ paying}
\displaystyle 8\%\text{ dividend. At the end of one year he sells the shares at a premium of Rs. }20.\text{ Find:}
\displaystyle \text{(i) The annual dividend.}
\displaystyle \text{(ii) The profit earned including his dividend.}\hspace{0.2cm}\text{[ICSE 2011]}
\displaystyle \text{Answer:}
\displaystyle \text{Face value of each share}=\text{Rs. }100
\displaystyle \text{Market value at discount of Rs. }20=100-20=80
\displaystyle \text{Number of shares bought}=\frac{52000}{80}=650
\displaystyle \text{Dividend on one share}=8\%\text{ of }100
\displaystyle =\frac{8}{100}\times100=8
\displaystyle \text{Annual dividend}=650\times8=5200
\displaystyle \therefore \text{(i) Annual dividend = Rs. }5200
\displaystyle \text{Selling price of each share at premium of Rs. }20=100+20=120
\displaystyle \text{Total selling price}=650\times120=78000
\displaystyle \text{Profit on selling shares}=78000-52000=26000
\displaystyle \text{Total profit including dividend}=26000+5200
\displaystyle =31200
\displaystyle \therefore \text{(ii) Profit earned including dividend = Rs. }31200
\\

\displaystyle \textbf{Question 35. }\text{Ajay owns }560\text{ shares of a company. The face value of each share is Rs. }25.
\displaystyle \text{The company declares a dividend of }9\%.\text{ Calculate:} \hspace{0.2cm}\text{[ICSE 2007]}
\displaystyle \text{(i) The dividend that Ajay will get.}
\displaystyle \text{(ii) The rate of interest on his investment, if Ajay had paid Rs. }30\text{ for each share.}
\displaystyle \text{Answer:}
\displaystyle \text{Face value of each share}=\text{Rs. }25
\displaystyle \text{Dividend on one share}=9\%\text{ of }25
\displaystyle =\frac{9}{100}\times25=2.25
\displaystyle \text{Dividend on }560\text{ shares}=560\times2.25
\displaystyle =1260
\displaystyle \therefore \text{(i) Dividend that Ajay will get = Rs. }1260
\displaystyle \text{Investment}=560\times30=16800
\displaystyle \text{Rate of interest}=\frac{1260}{16800}\times100
\displaystyle =7.5\%
\displaystyle \therefore \text{(ii) Rate of interest on investment}=7.5\%
\\

\displaystyle \textbf{Question 36. }\text{A man bought }1000\text{ shares each of face value Rs. }5\text{ at Rs. }7\text{ per share. At}
\displaystyle \text{the end of the year the company declared a dividend of }8\%.\text{ Calculate:} \hspace{0.2cm}\text{[ICSE 1986]}
\displaystyle \text{(i) The amount of money invested by the man.}
\displaystyle \text{(ii) The percentage return on his outlay correct to one decimal place.}
\displaystyle \text{Answer:}
\displaystyle \text{Number of shares}=1000
\displaystyle \text{Market value of each share}=\text{Rs. }7
\displaystyle \text{Total investment}=1000\times7=7000
\displaystyle \therefore \text{(i) Amount invested = Rs. }7000
\displaystyle \text{Face value of each share}=\text{Rs. }5
\displaystyle \text{Dividend on one share}=8\%\text{ of }5
\displaystyle =\frac{8}{100}\times5=0.40
\displaystyle \text{Total dividend}=1000\times0.40=400
\displaystyle \text{Percentage return}=\frac{400}{7000}\times100
\displaystyle =5.714\%
\displaystyle \approx 5.7\%
\displaystyle \therefore \text{(ii) Percentage return on outlay}=5.7\%
\\

\displaystyle \textbf{Question 37. }\text{A man bought }500\text{ shares, each of face value Rs. }10\text{ of a certain business}
\displaystyle \text{concern, and during the first year after purchase received Rs. }400\text{ as dividend}
\displaystyle \text{on his shares. Find the rate of dividend on his shares.} \hspace{0.2cm}\text{[ICSE 1987]}
\displaystyle \text{Answer:}
\displaystyle \text{Total face value of shares}=500\times10=5000
\displaystyle \text{Dividend received}=400
\displaystyle \text{Rate of dividend}=\frac{400}{5000}\times100
\displaystyle =8\%
\displaystyle \therefore \text{Rate of dividend}=8\%
\\

\displaystyle \textbf{Question 38. }\text{A man invests a sum of money in Rs. }100\text{ shares, paying }15\%\text{ dividend,}
\displaystyle \text{quoted at }20\%\text{ premium. If his annual dividend is Rs. }540,\text{ calculate:} \hspace{0.2cm}\text{[ICSE 1996]}
\displaystyle \text{(i) his total investment}
\displaystyle \text{(ii) the rate of return on his investment.}
\displaystyle \text{Answer:}
\displaystyle \text{Dividend on one share}=15\%\text{ of }100=15
\displaystyle \text{Number of shares}=\frac{540}{15}=36
\displaystyle \text{Market value of each share}=100+20\%\text{ of }100
\displaystyle =120
\displaystyle \text{Total investment}=36\times120=4320
\displaystyle \therefore \text{(i) Total investment = Rs. }4320
\displaystyle \text{Rate of return}=\frac{540}{4320}\times100
\displaystyle =12.5\%
\displaystyle \therefore \text{(ii) Rate of return on investment}=12.5\%
\\

\displaystyle \textbf{Question 39. }\text{A man invests Rs. }1800\text{ in buying shares of nominal value Rs. }24\text{ and selling}
\displaystyle \text{at }25\%\text{ premium. The dividend on the shares is }15\%\text{ per annum.} \hspace{0.2cm}\text{[ICSE 1999]}
\displaystyle \text{(i) Calculate the number of shares he buys.}
\displaystyle \text{(ii) Calculate the dividend he receives annually.}
\displaystyle \text{Answer:}
\displaystyle \text{Market value of each share}=24+25\%\text{ of }24
\displaystyle =24+6=30
\displaystyle \text{Number of shares bought}=\frac{1800}{30}=60
\displaystyle \therefore \text{(i) Number of shares bought}=60
\displaystyle \text{Dividend on one share}=15\%\text{ of }24
\displaystyle =\frac{15}{100}\times24=3.60
\displaystyle \text{Annual dividend}=60\times3.60=216
\displaystyle \therefore \text{(ii) Annual dividend received = Rs. }216
\\

\displaystyle \textbf{Question 40. }\text{A dividend of }9\%\text{ was declared on Rs. }100\text{ shares at a certain price. If the}
\displaystyle \text{rate of return is }7.5\%,\text{ calculate:} \hspace{0.2cm}\text{[ICSE 2000]}
\displaystyle \text{(i) the market value of the share.}
\displaystyle \text{(ii) the amount to be invested to obtain an annual dividend of Rs. }630.
\displaystyle \text{Answer:}
\displaystyle \text{Dividend on one share}=9\%\text{ of }100=9
\displaystyle \text{Let the market value of one share be Rs. }x
\displaystyle \frac{9}{x}\times100=7.5
\displaystyle x=\frac{9\times100}{7.5}=120
\displaystyle \therefore \text{(i) Market value of each share = Rs. }120
\displaystyle \text{Number of shares required}=\frac{630}{9}=70
\displaystyle \text{Amount to be invested}=70\times120=8400
\displaystyle \therefore \text{(ii) Amount to be invested = Rs. }8400
\\

\displaystyle \textbf{Question 41. }\text{A man invests Rs. }8800\text{ on buying shares of face value of rupees hundred}
\displaystyle \text{each at a premium of }10\%\text{ in a company. If he earns Rs. }1200\text{ at the end of}
\displaystyle \text{the year as dividend, find:} \hspace{0.2cm}\text{[ICSE 2001]}
\displaystyle \text{(i) the number of shares he has in the company.}
\displaystyle \text{(ii) What is the dividend percentage per share?}
\displaystyle \text{Answer:}
\displaystyle \text{Face value of each share}=\text{Rs. }100
\displaystyle \text{Market value of each share}=100+10\%\text{ of }100=110
\displaystyle \text{Number of shares bought}=\frac{8800}{110}=80
\displaystyle \therefore \text{(i) Number of shares}=80
\displaystyle \text{Dividend on one share}=\frac{1200}{80}=15
\displaystyle \text{Dividend percentage}=\frac{15}{100}\times100=15\%
\displaystyle \therefore \text{(ii) Dividend percentage per share}=15\%
\\

\displaystyle \textbf{Question 42. }\text{A man wants to buy }62\text{ shares available at Rs. }132\text{, par value of Rs. }100.
\displaystyle \text{(i) How much should he invest?} \hspace{0.2cm}\text{[ICSE 2002]}
\displaystyle \text{(ii) If the dividend is }7.5\%,\text{ what will be his annual income?}
\displaystyle \text{(iii) If he wants to increase his annual income by Rs. }150,\text{ how many extra shares should he buy?}
\displaystyle \text{Answer:}
\displaystyle \text{Market value of each share}=\text{Rs. }132
\displaystyle \text{Amount invested}=62\times132=8184
\displaystyle \therefore \text{(i) Amount invested = Rs. }8184
\displaystyle \text{Dividend on one share}=7.5\%\text{ of }100
\displaystyle =\frac{7.5}{100}\times100=7.5
\displaystyle \text{Annual income}=62\times7.5=465
\displaystyle \therefore \text{(ii) Annual income = Rs. }465
\displaystyle \text{Extra shares required}=\frac{150}{7.5}=20
\displaystyle \therefore \text{(iii) Extra shares required}=20
\\

\displaystyle \textbf{Question 43. }\text{A man invests Rs. }20020\text{ in buying shares of nominal value Rs. }26\text{ at }10\%
\displaystyle \text{premium. The dividend on the shares is }15\%\text{ per annum. Calculate:} \hspace{0.2cm}\text{[ICSE 2003]}
\displaystyle \text{(i) The number of shares he buys.}
\displaystyle \text{(ii) The dividend he receives annually.}
\displaystyle \text{(iii) The rate of interest he gets on his money.}
\displaystyle \text{Answer:}
\displaystyle \text{Nominal value of each share}=\text{Rs. }26
\displaystyle \text{Market value of each share}=26+10\%\text{ of }26
\displaystyle =26+2.60=28.60
\displaystyle \text{Number of shares bought}=\frac{20020}{28.60}=700
\displaystyle \therefore \text{(i) Number of shares bought}=700
\displaystyle \text{Dividend on one share}=15\%\text{ of }26
\displaystyle =\frac{15}{100}\times26=3.90
\displaystyle \text{Annual dividend}=700\times3.90=2730
\displaystyle \therefore \text{(ii) Annual dividend = Rs. }2730
\displaystyle \text{Rate of interest}=\frac{2730}{20020}\times100
\displaystyle =13.636\%
\displaystyle \approx 13.64\%
\displaystyle \therefore \text{(iii) Rate of interest}=13.64\%
\\

\displaystyle \textbf{Question 44. }\text{Mr. Kapoor invested Rs. }8000\text{ in }7\%\text{ hundred-rupee shares at Rs. }80. \text{ After a}
\displaystyle \text{year he sold these shares at Rs. }75\text{ each and invested the proceeds and also}
\displaystyle \text{the dividend in }18\%\text{ twenty-five-rupee shares at Rs. }41\text{ each. Calculate:}
\displaystyle \text{(i) his gain or loss after a year.} \hspace{0.2cm}\text{[ICSE 2006]}
\displaystyle \text{(ii) his annual income from the second investment.}
\displaystyle \text{(iii) the percentage of increase in return on his original investment.}
\displaystyle \text{Answer:}
\displaystyle \text{Number of first shares bought}=\frac{8000}{80}=100
\displaystyle \text{Dividend on one share}=7\%\text{ of }100=7
\displaystyle \text{Dividend received}=100\times7=700
\displaystyle \text{Sale value of shares}=100\times75=7500
\displaystyle \text{Total amount available for reinvestment}=7500+700=8200
\displaystyle \text{Gain/Loss}=8200-8000=200
\displaystyle \therefore \text{(i) Gain after one year = Rs. }200
\displaystyle \text{Number of second shares bought}=\frac{8200}{41}=200
\displaystyle \text{Dividend on one second share}=18\%\text{ of }25
\displaystyle =\frac{18}{100}\times25=4.50
\displaystyle \text{Annual income from second investment}=200\times4.50
\displaystyle =900
\displaystyle \therefore \text{(ii) Annual income from second investment = Rs. }900
\displaystyle \text{Original annual income}=700
\displaystyle \text{Increase in income}=900-700=200
\displaystyle \text{Percentage increase}=\frac{200}{8000}\times100
\displaystyle =2.5\%
\displaystyle \therefore \text{(iii) Percentage increase in return on original investment}=2.5\%
\\

\displaystyle \textbf{Question 45. }\text{A man invested Rs. }45000\text{ in }15\%\text{ Rs. }100\text{ shares quoted at Rs. }125. \text{ When}
\displaystyle \text{the market value of these shares rose to Rs. }140\text{, he sold some shares, just}
\displaystyle \text{enough to raise Rs. }8400.\text{ Calculate:} \hspace{0.2cm}\text{[ICSE 2004]}
\displaystyle \text{(i) the number of shares he still holds.}
\displaystyle \text{(ii) the dividend due to him on these remaining shares.}
\displaystyle \text{Answer:}
\displaystyle \text{Number of shares purchased}=\frac{45000}{125}=360
\displaystyle \text{Number of shares sold}=\frac{8400}{140}=60
\displaystyle \text{Remaining shares}=360-60=300
\displaystyle \therefore \text{(i) Number of shares still held}=300
\displaystyle \text{Dividend on one share}=15\%\text{ of }100=15
\displaystyle \text{Dividend due}=300\times15
\displaystyle =4500
\displaystyle \therefore \text{(ii) Dividend due = Rs. }4500
\\

\displaystyle \textbf{Question 46. }\text{Mr. Tiwari invested Rs. }29040\text{ in }15\%\text{ Rs. }100\text{ shares quoted at a premium}
\displaystyle \text{of }20\%.\text{ Calculate:} \hspace{0.2cm}\text{[ICSE 2005]}
\displaystyle \text{(i) The number of shares bought by Mr. Tiwari.}
\displaystyle \text{(ii) Mr. Tiwari's income from the investment.}
\displaystyle \text{(iii) The percentage return on his investment.}
\displaystyle \text{Answer:}
\displaystyle \text{Market value of one share}=100+20\%\text{ of }100
\displaystyle =120
\displaystyle \text{Number of shares bought}=\frac{29040}{120}=242
\displaystyle \therefore \text{(i) Number of shares bought}=242
\displaystyle \text{Dividend on one share}=15\%\text{ of }100=15
\displaystyle \text{Annual income}=242\times15=3630
\displaystyle \therefore \text{(ii) Annual income = Rs. }3630
\displaystyle \text{Percentage return}=\frac{3630}{29040}\times100
\displaystyle =12.5\%
\displaystyle \therefore \text{(iii) Percentage return on investment}=12.5\%
\\

\displaystyle \textbf{Question 47. }\text{Amit Kumar invests Rs. }36000\text{ in buying Rs. }100\text{ shares at Rs. }20\text{ premium.}
\displaystyle \text{The dividend is }15\%\text{ per annum. Find:} \hspace{0.2cm}\text{[ICSE 2009]}
\displaystyle \text{(i) The number of shares he buys.}
\displaystyle \text{(ii) His yearly dividend.}
\displaystyle \text{(iii) The percentage return on his investment. Give your answer correct to the}
\displaystyle \text{nearest whole number.}
\displaystyle \text{Answer:}
\displaystyle \text{Market value of one share}=100+20=120
\displaystyle \text{Number of shares bought}=\frac{36000}{120}=300
\displaystyle \therefore \text{(i) Number of shares bought}=300
\displaystyle \text{Dividend on one share}=15\%\text{ of }100=15
\displaystyle \text{Yearly dividend}=300\times15=4500
\displaystyle \therefore \text{(ii) Yearly dividend = Rs. }4500
\displaystyle \text{Percentage return}=\frac{4500}{36000}\times100
\displaystyle =12.5\%
\displaystyle \approx 13\%
\displaystyle \therefore \text{(iii) Percentage return on investment}=13\%
\\

\displaystyle \textbf{Question 48. }\text{A man invests Rs. }11200\text{ in a company paying }6\%\text{ dividend when its Rs. }100
\displaystyle \text{share can be bought at a premium of }40\%.\text{ Find:} \hspace{0.2cm}\text{[ICSE 1998]}
\displaystyle \text{(i) his annual income}
\displaystyle \text{(ii) his percentage income on his investment.}
\displaystyle \text{Answer:}
\displaystyle \text{Face value of each share}=\text{Rs. }100
\displaystyle \text{Market value of each share}=100+40\%\text{ of }100=140
\displaystyle \text{Number of shares bought}=\frac{11200}{140}=80
\displaystyle \text{Dividend on one share}=6\%\text{ of }100=6
\displaystyle \text{Annual income}=80\times6=480
\displaystyle \therefore \text{Annual income = Rs. }480
\displaystyle \text{Percentage income}=\frac{480}{11200}\times100
\displaystyle =4.2857\%
\displaystyle \approx 4.29\%
\displaystyle \therefore \text{Percentage income on investment}=4.29\%
\\

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