\displaystyle \textbf{Question 1: } \text{Calculate the money required to buy:}
\displaystyle \text{(i) }350,\ \text{Rs. }20\text{ shares at a premium of Rs. }7
\displaystyle \text{(ii) }275,\ \text{Rs. }60\text{ shares at a discount of Rs. }10
\displaystyle \text{(iii) }50,\ \text{Rs. }75\text{ shares quoted at Rs. }71.50
\displaystyle \text{Answer:}

\displaystyle \text{(i) Market price of one share}=20+7=\text{Rs. }27
\displaystyle \text{Money required}=350\times27=\text{Rs. }9450

\displaystyle \text{(ii) Market price of one share}=60-10=\text{Rs. }50
\displaystyle \text{Money required}=275\times50=\text{Rs. }13750

\displaystyle \text{(iii) Quoted price of a share is its market price.}
\displaystyle \text{Market price of one share}=\text{Rs. }71.50
\displaystyle \text{Money required}=50\times71.50=\text{Rs. }3575
\\

\displaystyle \textbf{Question 2: } \text{Ravi invested Rs. }6250\text{ in shares of a company paying }6\%
\displaystyle \text{dividend per annum. If he bought Rs. }25\text{ shares for Rs. }31.25\text{ each,}
\displaystyle \text{find his income from the investment.}
\displaystyle \text{Answer:}
\displaystyle \text{Market price of one share}=\text{Rs. }31.25
\displaystyle \text{Number of shares bought}=\frac{6250}{31.25}=200
\displaystyle \text{Dividend on one share}=25\times\frac{6}{100}=\text{Rs. }1.50
\displaystyle \therefore \text{Annual income}=200\times1.50=\text{Rs. }300
\\

\displaystyle \textbf{Question 3: } \text{Manoj buys Rs. }100\text{ shares at a premium of Rs. }20\text{ in a}
\displaystyle \text{company paying }15\%\text{ dividend. Find: (i) The market value of }200\text{ shares}
\displaystyle \text{(ii) His annual income \quad (iii) His percentage income.}
\displaystyle \text{Answer:}
\displaystyle \text{(i) Market price of one share}=100+20=\text{Rs. }120
\displaystyle \text{Market value of }200\text{ shares}=200\times120=\text{Rs. }24000
\displaystyle \text{(ii) Annual income}=200\times100\times\frac{15}{100}=\text{Rs. }3000
\displaystyle \text{(iii) Percentage income}=\frac{3000}{24000}\times100=12.5\%
\\

\displaystyle \textbf{Question 4: } \text{Rs. }67200\text{ are invested in Rs. }100\text{ shares which are quoted}
\displaystyle \text{at Rs. }120.\text{ Find the income if }12\%\text{ dividend is declared on the shares.}
\displaystyle \hfill \text{[ICSE 1982]}
\displaystyle \text{Answer:}
\displaystyle \text{Amount invested}=\text{Rs. }67200
\displaystyle \text{Market price of one share}=\text{Rs. }120
\displaystyle \text{Number of shares bought}=\frac{67200}{120}=560
\displaystyle \text{Dividend on one share}=100\times\frac{12}{100}=\text{Rs. }12
\displaystyle \therefore \text{Annual income}=560\times12=\text{Rs. }6720
\\

\displaystyle \textbf{Question 5: } \text{Find the dividend due at the end of a year on }250\text{ shares of}
\displaystyle \text{Rs. }50\text{ each, if the half-yearly dividend is }4\%\text{ of the value of the share.}
\displaystyle \hfill \text{[ICSE 1983]}
\displaystyle \text{Answer:}
\displaystyle \text{Half-yearly dividend on one share}=4\%\text{ of Rs. }50=\frac{4}{100}\times50=\text{Rs. }2
\displaystyle \text{Yearly dividend on one share}=2\times2=\text{Rs. }4
\displaystyle \therefore \text{Total yearly dividend}=250\times4=\text{Rs. }1000
\\

\displaystyle \textbf{Question 6: } \text{A man bought }500\text{ shares, each of face value Rs. }10,\text{ of a}
\displaystyle \text{certain business concern and during the first year after purchase,}
\displaystyle \text{received Rs. }400\text{ as dividend on his shares. Find the rate of dividend.}
\displaystyle \hfill \text{[ICSE 1985]}
\displaystyle \text{Answer:}
\displaystyle \text{Face value of one share}=\text{Rs. }10
\displaystyle \text{Number of shares}=500
\displaystyle \text{Total face value}=500\times10=\text{Rs. }5000
\displaystyle \text{Let the rate of dividend be }x\%
\displaystyle 5000\times\frac{x}{100}=400
\displaystyle 50x=400
\displaystyle x=8
\displaystyle \therefore \text{Rate of dividend}=8\%
\\

\displaystyle \textbf{Question 7: } \text{Mukul invests Rs. }9000\text{ in a company paying a dividend of }6\%
\displaystyle \text{per annum when a share of face value Rs. }100\text{ stands at Rs. }150.
\displaystyle \text{What is his annual income? If he sells }50\%\text{ of his shares when the}
\displaystyle \text{price rises to Rs. }200,\text{ what is his gain in this transaction?}
\displaystyle \hfill \text{[ICSE 1991]}
\displaystyle \text{Answer:}
\displaystyle \text{Market price of one share}=\text{Rs. }150
\displaystyle \text{Number of shares bought}=\frac{9000}{150}=60
\displaystyle \text{Dividend on one share}=100\times\frac{6}{100}=\text{Rs. }6
\displaystyle \text{Annual income}=60\times6=\text{Rs. }360
\displaystyle \text{Number of shares sold}=50\%\text{ of }60=30
\displaystyle \text{Sale proceeds}=30\times200=\text{Rs. }6000
\displaystyle \text{Cost price of these shares}=30\times150=\text{Rs. }4500
\displaystyle \therefore \text{Gain}=6000-4500=\text{Rs. }1500
\\

\displaystyle \textbf{Question 8: } \text{A man wants to buy }62\text{ shares available at Rs. }132
\displaystyle \text{(par value being Rs. }100\text{). Find: (i) How much he will have to invest}
\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}
\displaystyle \text{extra shares should he buy? }\hfill \text{[ICSE 2002]}
\displaystyle \text{Answer:}
\displaystyle \text{(i) Investment}=62\times132=\text{Rs. }8184
\displaystyle \text{(ii) Dividend on one share}=100\times\frac{7.5}{100}=\text{Rs. }7.50
\displaystyle \text{Annual income}=62\times7.50=\text{Rs. }465
\displaystyle \text{(iii) Additional shares required}=\frac{150}{7.50}=20
\displaystyle \therefore \text{He should buy }20\text{ more shares.}
\\

\displaystyle \textbf{Question 9: } \text{A company with }4000\text{ shares of nominal value Rs. }110
\displaystyle \text{each 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 Shah Rukh who holds }88\text{ shares}
\displaystyle \text{(iii) If he received only }10\%\text{ on his investment, find the price}
\displaystyle \text{Shah Rukh paid for each share. }\hfill \text{[ICSE 2008]}
\displaystyle \text{Answer:}
\displaystyle \text{(i) Dividend on one share}=110\times\frac{15}{100}=\text{Rs. }16.50
\displaystyle \text{Total dividend paid}=4000\times16.50=\text{Rs. }66000
\displaystyle \text{(ii) Annual income of Shah Rukh}=88\times16.50=\text{Rs. }1452
\displaystyle \text{(iii) Let the price paid for one share be Rs. }x
\displaystyle x\times\frac{10}{100}=110\times\frac{15}{100}
\displaystyle \frac{10x}{100}=\frac{15\times110}{100}
\displaystyle x=165
\displaystyle \therefore \text{Price paid for each share}=\text{Rs. }165
\\

\displaystyle \textbf{Question 10: } \text{A man buys a Rs. }40\text{ share in a company which pays }10\%
\displaystyle \text{dividend. He buys the share at such a price that his profit is }16\%\text{ on his}
\displaystyle \text{investment. At what price did he buy the share?}
\displaystyle \text{Answer:}
\displaystyle \text{Dividend on one share}=40\times\frac{10}{100}=\text{Rs. }4
\displaystyle \text{Let the market price of one share}=\text{Rs. }x
\displaystyle \text{Since the return on investment is }16\%,
\displaystyle \frac{16x}{100}=4
\displaystyle x=25
\displaystyle \therefore \text{He bought each share for Rs. }25
\\

\displaystyle \textbf{Question 11: } \text{Ajay owns }560\text{ shares of a company. The face value of each}
\displaystyle \text{share is Rs. }25.\text{ The company declares a dividend of }9\%.\text{ Calculate:}
\displaystyle \text{(i) The dividend that Ajay will get \quad (ii) The rate of return on his}
\displaystyle \text{investment, if Ajay had paid Rs. }30\text{ for each share.}
\displaystyle \text{Answer:}
\displaystyle \text{(i) Dividend on one share}=25\times\frac{9}{100}=\text{Rs. }2.25
\displaystyle \text{Total dividend}=560\times2.25=\text{Rs. }1260
\displaystyle \text{(ii) Let the rate of return be }x\%
\displaystyle x\%\text{ of Rs. }30=9\%\text{ of Rs. }25
\displaystyle \frac{x}{100}\times30=\frac{9}{100}\times25
\displaystyle x=7.5
\displaystyle \therefore \text{Rate of return}=7.5\%
\\

\displaystyle \textbf{Question 12: } \text{How much should a man invest in Rs. }50\text{ shares selling at}
\displaystyle \text{Rs. }60\text{ to obtain an annual income of Rs. }900,\text{ if the dividend}
\displaystyle \text{declared is }15\%\text{?}
\displaystyle \text{Answer:}
\displaystyle \text{Dividend on one share}=50\times\frac{15}{100}=\text{Rs. }7.50
\displaystyle \text{Number of shares required}=\frac{900}{7.50}=120
\displaystyle \text{Market price of one share}=\text{Rs. }60
\displaystyle \therefore \text{Amount to be invested}=120\times60=\text{Rs. }7200
\\

\displaystyle \textbf{Question 13: } \text{A dividend of }9\%\text{ was declared on Rs. }100\text{ shares selling}
\displaystyle \text{at a certain price. If the rate of return is }7.5\%,\text{ calculate:}
\displaystyle \text{(i) The market value of the share \quad (ii) The amount to be invested}
\displaystyle \text{to obtain an annual dividend of Rs. }630.\hfill \text{[ICSE 2000]}
\displaystyle \text{Answer:}
\displaystyle \text{(i) Let the market value of one share}=\text{Rs. }x
\displaystyle \frac{7.5}{100}\times x=\frac{9}{100}\times100
\displaystyle x=120
\displaystyle \therefore \text{Market value of one share}=\text{Rs. }120
\displaystyle \text{(ii) Annual dividend on one share}=100\times\frac{9}{100}=\text{Rs. }9
\displaystyle \text{Number of shares required}=\frac{630}{9}=70
\displaystyle \therefore \text{Amount to be invested}=70\times120=\text{Rs. }8400
\\

\displaystyle \textbf{Question 14: } \text{Which is a better investment: }12\%\text{ Rs. }100\text{ shares at Rs. }120
\displaystyle \text{or }8\%\text{ Rs. }100\text{ shares at Rs. }90\text{?}
\displaystyle \text{Answer:}
\displaystyle \text{For }12\%\text{ Rs. }100\text{ shares at Rs. }120:
\displaystyle \text{Dividend on one share}=100\times\frac{12}{100}=\text{Rs. }12
\displaystyle \text{Percentage return}=\frac{12}{120}\times100=10\%
\displaystyle \text{For }8\%\text{ Rs. }100\text{ shares at Rs. }90:
\displaystyle \text{Dividend on one share}=100\times\frac{8}{100}=\text{Rs. }8
\displaystyle \text{Percentage return}=\frac{8}{90}\times100=8.89\%
\displaystyle \therefore \text{The first investment is better.}
\\

\displaystyle \textbf{Question 15: } \text{A man sells }60,\ \text{Rs. }15\text{ shares of a company paying }12\%
\displaystyle \text{dividend at Rs. }21\text{ each and invests the proceeds in Rs. }6\text{ shares}
\displaystyle \text{of another company at Rs. }9\text{ each. Find his change in income,}
\displaystyle \text{if the second company pays a dividend of }8\%.
\displaystyle \text{Answer:}
\displaystyle \text{Income from first investment}=60\times15\times\frac{12}{100}=\text{Rs. }108
\displaystyle \text{Sale proceeds}=60\times21=\text{Rs. }1260
\displaystyle \text{Number of new shares bought}=\frac{1260}{9}=140
\displaystyle \text{Income from second investment}=140\times6\times\frac{8}{100}=\text{Rs. }67.20
\displaystyle \text{Change in income}=108-67.20=\text{Rs. }40.80
\displaystyle \therefore \text{His annual income decreases by Rs. }40.80
\\

\displaystyle \textbf{Question 16: } \text{Mr. Ram Gopal invested Rs. }8000\text{ in }7\%\text{ Rs. }100\text{ shares}
\displaystyle \text{at Rs. }80.\text{ After a year he sold these shares at Rs. }75\text{ each and invested}
\displaystyle \text{the proceeds, including his dividend, in }18\%\text{ Rs. }25\text{ shares at Rs. }41.
\displaystyle \text{Find: (i) His dividend for the first year \quad (ii) His annual income in the}
\displaystyle \text{second year \quad (iii) The percentage increase in his return on his original investment.}
\displaystyle \hfill \text{[ICSE 2006]}
\displaystyle \text{Answer:}
\displaystyle \text{Number of shares bought}=\frac{8000}{80}=100
\displaystyle \text{Dividend for the first year}=100\times100\times\frac{7}{100}=\text{Rs. }700
\displaystyle \text{Sale proceeds, including dividend}=100\times75+700=\text{Rs. }8200
\displaystyle \text{Number of new shares bought}=\frac{8200}{41}=200
\displaystyle \text{Annual income in the second year}=200\times25\times\frac{18}{100}=\text{Rs. }900
\displaystyle \text{Increase in annual income}=900-700=\text{Rs. }200
\displaystyle \text{Percentage increase on original investment}=\frac{200}{8000}\times100=2.5\%
\\

\displaystyle \textbf{Question 17: } \text{Ashok and Sandeep invest Rs. }18000\text{ each in buying shares}
\displaystyle \text{of two different companies. Ashok buys }7.5\%\text{ Rs. }100\text{ shares at a}
\displaystyle \text{discount of }20\%,\text{ whereas Sandeep buys Rs. }50\text{ shares at a premium}
\displaystyle \text{of }20\%.\text{ If both receive equal dividend, find the rate of dividend received}
\displaystyle \text{by Sandeep.}
\displaystyle \text{Answer:}
\displaystyle \text{For Ashok:}
\displaystyle \text{Market price of one share}=100-20\%\text{ of }100=\text{Rs. }80
\displaystyle \text{Number of shares bought}=\frac{18000}{80}=225
\displaystyle \text{Dividend received}=225\times100\times\frac{7.5}{100}=\text{Rs. }1687.50
\displaystyle \text{For Sandeep:}
\displaystyle \text{Market price of one share}=50+20\%\text{ of }50=\text{Rs. }60
\displaystyle \text{Number of shares bought}=\frac{18000}{60}=300
\displaystyle \text{Let the rate of dividend received by Sandeep be }x\%.
\displaystyle 300\times50\times\frac{x}{100}=1687.50
\displaystyle 150x=1687.50
\displaystyle x=11.25
\displaystyle \therefore \text{Rate of dividend received by Sandeep}=11.25\%
\\

\displaystyle \textbf{Question 18: } \text{John had }1000\text{ shares of a company with face value Rs. }40
\displaystyle \text{and paying }8\%\text{ dividend. He sold some of these shares at a discount of }10\%
\displaystyle \text{and invested the proceeds in Rs. }20\text{ shares at a premium of }50\%\text{ and paying}
\displaystyle 12\%\text{ dividend. If the change in his income is Rs. }192,\text{ find the number}
\displaystyle \text{of shares sold by John.}
\displaystyle \text{Answer:}
\displaystyle \text{Let the number of shares sold by John be }x.
\displaystyle \text{Dividend on one old share}=40\times\frac{8}{100}=\text{Rs. }3.20
\displaystyle \text{Dividend lost on }x\text{ shares}=3.20x\text{ Rs.}
\displaystyle \text{Selling price of one old share}=40-10\%\text{ of }40=\text{Rs. }36
\displaystyle \text{Sale proceeds}=36x\text{ Rs.}
\displaystyle \text{Market price of one new share}=20+50\%\text{ of }20=\text{Rs. }30
\displaystyle \text{Number of new shares bought}=\frac{36x}{30}=1.2x
\displaystyle \text{Dividend on one new share}=20\times\frac{12}{100}=\text{Rs. }2.40
\displaystyle \text{Dividend from new shares}=1.2x\times2.40=2.88x\text{ Rs.}
\displaystyle \text{Given, change in income}=\text{Rs. }192
\displaystyle 3.20x-2.88x=192
\displaystyle 0.32x=192
\displaystyle x=600
\displaystyle \therefore \text{Number of shares sold by John}=600
\\

\displaystyle \textbf{Question 19: } \text{Divide Rs. }40608\text{ into two parts such that if one part}
\displaystyle \text{is invested in }8\%\text{ Rs. }100\text{ shares at }8\%\text{ discount and the other}
\displaystyle \text{part is invested in }9\%\text{ Rs. }100\text{ shares at }8\%\text{ premium, the annual}
\displaystyle \text{incomes from both investments are equal.}
\displaystyle \text{Answer:}
\displaystyle \text{Let the two parts be Rs. }x\text{ and Rs. }(40608-x).
\displaystyle \text{Market price of one first share}=100-8\%\text{ of }100=\text{Rs. }92
\displaystyle \text{Annual income from first investment}=\frac{x}{92}\times100\times\frac{8}{100}=\frac{2x}{23}
\displaystyle \text{Market price of one second share}=100+8\%\text{ of }100=\text{Rs. }108
\displaystyle \text{Annual income from second investment}=\frac{40608-x}{108}\times100\times\frac{9}{100}
\displaystyle =\frac{40608-x}{12}
\displaystyle \text{Since the annual incomes are equal,}
\displaystyle \frac{2x}{23}=\frac{40608-x}{12}
\displaystyle 24x=23(40608-x)
\displaystyle 24x=933984-23x
\displaystyle 47x=933984
\displaystyle x=19872
\displaystyle \therefore \text{First part}=\text{Rs. }19872
\displaystyle \text{Second part}=40608-19872=\text{Rs. }20736
\\

\displaystyle \textbf{Question 20: } \text{A man has a choice to invest in Rs. }100\text{ shares of two companies}
\displaystyle A\text{ and }B.\text{ Shares of company }A\text{ are available at a premium of }20\%
\displaystyle \text{and it pays }8\%\text{ dividend, whereas shares of company }B\text{ are available}
\displaystyle \text{at a discount of }10\%\text{ and it pays }7\%\text{ dividend. If the man invests}
\displaystyle \text{equally in both companies and the sum of the return from them is Rs. }936,
\displaystyle \text{find how much, in all, does he invest?}
\displaystyle \text{Answer:}
\displaystyle \text{Let the man invest Rs. }x\text{ in each company.}
\displaystyle \text{For company }A:
\displaystyle \text{Market price of one share}=100+20\%\text{ of }100=\text{Rs. }120
\displaystyle \text{Dividend on one share}=100\times\frac{8}{100}=\text{Rs. }8
\displaystyle \text{Total dividend from company }A=\frac{x}{120}\times8=\frac{x}{15}
\displaystyle \text{For company }B:
\displaystyle \text{Market price of one share}=100-10\%\text{ of }100=\text{Rs. }90
\displaystyle \text{Dividend on one share}=100\times\frac{7}{100}=\text{Rs. }7
\displaystyle \text{Total dividend from company }B=\frac{x}{90}\times7=\frac{7x}{90}
\displaystyle \text{Given, }\frac{x}{15}+\frac{7x}{90}=936
\displaystyle \frac{6x+7x}{90}=936
\displaystyle \frac{13x}{90}=936
\displaystyle x=\frac{936\times90}{13}=\text{Rs. }6480
\displaystyle \therefore \text{Total investment}=2\times6480=\text{Rs. }12960
\\

Discover more from ICSE / ISC / CBSE Mathematics Portal for K12 Students

Subscribe to get the latest posts sent to your email.