Question 1: A man invests Rs. 8,800 in buying shares of a company of face value of Rs. 100 each at a premium of 10%. If he ears Rs. 1,200 at the end of the year as dividend. Find; i) The number of shares he has in the company. ii) The dividend percent per share.      [ICSE2001]
\displaystyle \text{Answer:}
\displaystyle \text{Nominal price of the share } = 100 \text{ Rs. }
\displaystyle \text{Cost price of the share } = 100 + 10 = 110 \text{ Rs. }
\displaystyle \text{Number of shares bought } = \frac{8800}{110} = 80
\displaystyle \text{Dividend earned } = 1200 \text{ Rs. }
\displaystyle \text{Let the dividend } % = x Therefore
\displaystyle 80 \times 100 \times \frac{x}{100} = 1200 \Rightarrow x = 15%

Question 2: A man invests Rs. 1680 in buying shares of nominal value Rs. 24 and selling at 12% premium. The dividend on the shares is 15% per annum. Calculate: i) The number of shares he buys; ii) The dividend he receives.      [ICSE1999]
\displaystyle \text{Answer:}
\displaystyle \text{Nominal price of the share } = 24 \text{ Rs. }
\displaystyle \text{Selling price of the share } = 24 + 24 \times \frac{12}{100} = 26.88 \text{ Rs. }
\displaystyle \text{Number of shares bought } = \frac{1680}{26.88} = 62.5
\displaystyle \text{Dividend received } = 62.5 \times 24 \times \frac{15}{100} = 225 \text{ Rs. }

Question 3: By investing Rs. 7500 in a company paying 10% dividend, an annual income of Rs. 500 is received. What price is paid for each of Rs.100 shares?       [1990]
\displaystyle \text{Answer:}
Let the premium \displaystyle = x \text{ Rs. }
Market price \displaystyle = (100 + x) \text{ Rs. }
Therefore
\displaystyle \frac{7500}{(100 + x)} \times 100 \times \frac{10}{100} = 500
\displaystyle 750 = 500 + 5x
\displaystyle x = 50
Hence the price paid for each share \displaystyle = 100 + 50 = 150 \text{ Rs. }

Question 4: A man invests Rs. 20,020 in buying shares of N.V. Rs. 26 at 10% premium. The dividend on the shares is 15% per annum. Calculate: i) The number of shares he buys; ii) The dividend he receives annually; iii) The rate of interest he gets on his money.       [ICSE2012]
\displaystyle \text{Answer:}
\displaystyle \text{Number of shares } = \frac{20020}{26 + 2.6} = 700
\displaystyle \text{Dividend } = 700 \times 26 \times \frac{15}{100} = 2730 \text{ Rs. }
\displaystyle \text{rate of interest he gets} = \frac{2730}{20020} \times 100 = 13.64%

Question 5: A man invested Rs. 45,000 in 15% Rs.100 shares quoted at Rs. 125, when the M.V. of these shares rose to Rs. 140, he sold some shares, just enough to raise Rs. 8400. calculate: i) The number of shares he still holds; ii) The dividend due to him on these remaining shares.       [ICSE2004]
\displaystyle \text{Answer:}
\displaystyle \text{Nominal Value of the share } = 100 \text{ Rs. }
\displaystyle \text{Market Value of the share } = 125 \text{ Rs. }
\displaystyle \text{Number of shares bought } = \frac{45000}{125} = 360
Selling Value of the share \displaystyle = 140 \text{ Rs. }
Amount of money raised \displaystyle = 8400 \text{ Rs. }
Therefore number of shares sold \displaystyle = \frac{8400}{140} = 60
Shares left \displaystyle = 360 - 60 = 300
\displaystyle \text{Dividend earned on remaining shares } = 300 \times 100 \times \frac{15}{100} = 4500 \text{ Rs. }

Question 6: Vivek invests Rs. 4,500 in 8%, Rs.10 shares at Rs. 15. He sells the shares when the price rises to Rs. 30, and invests the proceeds in 12% Rs. 100 shares at Rs. 125. Calculate; i) The sale proceeds ii) The number of Rs. 125 shares he buys; iii) The change in his annual income from dividend.       [ICSE2010]
\displaystyle \text{Answer:}
First Investment
Let the amount invested \displaystyle = 4500 \text{ Rs. }
\displaystyle \text{Nominal Value of the share } = 10 \text{ Rs. }
\displaystyle \text{Market Value of the share } = 15 \text{ Rs. }
\displaystyle \text{Dividend earned } = 8%
\displaystyle \text{Number of shares bought } = \frac{4500}{15} = 300
Sale Proceed \displaystyle = 300 \times 30 = 9000 \text{ Rs. }
\displaystyle \text{Dividend earned } = 300 \times 10 \times \frac{8}{100} = 240 \text{ Rs. }
Second Investment
Therefore the amount invested \displaystyle = 9000 \text{ Rs. }
\displaystyle \text{Nominal Value of the share } = 100 \text{ Rs. }
\displaystyle \text{Market Value of the share } = 125 \text{ Rs. }
\displaystyle \text{Dividend earned } = 12%
\displaystyle \text{Number of shares bought } = \frac{9000}{125} = 72
\displaystyle \text{Dividend earned } = 72 \times 100 \times \frac{12}{100} = 864 \text{ Rs. }
Hence the change in income \displaystyle = 864 - 240 = 624 \text{ Rs. }

Question 7: Mr. Parekh invested Rs. 52,000 on Rs. 100 shares at a discount of Rs. 20 paying 8% dividend. At the end of one year he sells the shares at a premium of Rs. 20; find: i) The annual dividend; ii) The profit earned including his dividend.      [ICSE2011]
\displaystyle \text{Answer:}
\displaystyle \text{Nominal Value of the share } = 100 \text{ Rs. }
\displaystyle \text{Market Value of the share } = 80 \text{ Rs. }
\displaystyle \text{Number of shares bought } = \frac{52000}{80} = 650
\displaystyle \text{Dividend earned } = 650 \times 100 \times \frac{8}{100} = 5200 \text{ Rs. }
\displaystyle \text{Sale proceeds } = 650 \times 120 = 78000 \text{ Rs. }
\displaystyle \text{Profit } = (78000 - 52000) + 5200 = 31200 \text{ Rs. }

Question 8: Salman buys 50 shares of face value Rs. 100 available at Rs. 132. i) What is his investment? ii) If the dividend is 7.5%, what will be his annual income? iii) If he wants to increase his annual income by Rs. 150, how many extra shares should he buy?       [ICSE2013]
\displaystyle \text{Answer:}
\displaystyle \text{Nominal Value of the share } = 100 \text{ Rs. }
\displaystyle \text{Market Value of the share } = 132 \text{ Rs. }
\displaystyle \text{Number of shares bought } = 50
\displaystyle \text{Investment } = 50 \times 132 = 6600 \text{ Rs. }
\displaystyle \text{Dividend earned } = 50 \times 100 \times \frac{7.5}{100} = 375 \text{ Rs. }
\displaystyle \text{Dividend earned on 1 share } = 1 \times 100 \times \frac{7.5}{100} = 7.5 \text{ Rs. }
\displaystyle \text{Therefore to earn 150 Rs. more, one needs to buy } \frac{150}{7.5} = 20 \text{ shares.}

Question 9: Salman invests a sum of money in Rs. 50 shares, paying 15% dividend quoted at 20% premium. If his annual dividend is Rs. 600, Calculate; i) The number of shares he bought; ii) His total investment; ii) The rate of return on his investment.      [ICSE2004]
Answer:
\displaystyle \text{Nominal Value of the share } = 50 \text{ Rs. }
\displaystyle \text{Market Value of the share } = 60 \text{ Rs. }
\displaystyle \text{Dividend earned } = 15%
\displaystyle \text{Dividend earned on 1 share } = 1 \times 50 \times \frac{15}{100} = 7.5 \text{ Rs. }
\displaystyle \text{Number of shares bought } = \frac{600}{7.5} = 80
\displaystyle \text{Investment } = 80 \times 60 = 4800 \text{ Rs. }
\displaystyle \text{return } = \frac{600}{4800} \times 100 = 12.5%

Question 10: The sum invested to purchase 15 shares of a company of nominal value \displaystyle \text{Rs }75 available at a discount of \displaystyle 20\% is                   [ICSE 2024]
(a) \displaystyle \text{Rs }60 \qquad
(b) \displaystyle \text{Rs }90 \qquad
(c) \displaystyle \text{Rs }1350 \qquad
(d) \displaystyle \text{Rs }900
\displaystyle \text{Answer:}
\displaystyle 1.\ (d)\ \text{Given, number of shares} = 15
\displaystyle \text{Nominal value per share} = \text{Rs }75
\displaystyle \text{Rate of discount} = 20\%
\displaystyle \therefore\ \text{Invested sum} = 15 \times 75 \times \frac{4}{5} = \text{Rs }900

 

Question 11: Mr. Gupta invested \displaystyle \text{Rs }3300 in buying \displaystyle \text{Rs }100 shares of a company at \displaystyle 10\% premium. The dividend declared by the company is \displaystyle 12\%. Find
(i) the number of shares purchased by him.
(ii) his annual dividend.
[ICSE 2024]
\displaystyle \text{Answer:}
\displaystyle 2.\ \text{Given, invested amount} = \text{Rs }3300
\displaystyle \text{Value for each share} = \text{Rs }100 = \text{Nominal value}
\displaystyle \text{Rate of premium} = 10\%
\displaystyle \text{Dividend declared by the company} = 12\%
\displaystyle (i)\ \text{Market value of one share} = 100 + \frac{10}{100}\times 100 = 100 + 10 = \text{Rs }110
\displaystyle \text{Number of shares} = \frac{\text{Money invested}}{\text{Market value for each share}} = \frac{3300}{110} = 30
\displaystyle (ii)\ \text{Annual dividend} = \text{Number of shares} \times \text{Rate of dividend} \times \text{Nominal value}
\displaystyle = 30 \times 12\% \times 100 = \text{Rs }3600

Question 12: Mr. Sharma receives an annual income of \displaystyle \text{Rs }900 in buying \displaystyle \text{Rs }50 shares selling at
\displaystyle \text{Rs }80. If the dividend declared is \displaystyle 20\%, find
(i) amount invested by Mr. Sharma.
(ii) percentage return on his investment.
[ICSE 2020]
\displaystyle \text{Answer:}
\displaystyle 3.\ \text{Given, dividend} = \text{Rs }900,\ \text{face value} = \text{Rs }50\ \text{and market value} = \text{Rs }80
\displaystyle \text{Let the number of shares be }n.
\displaystyle \text{Then, } n \times 50 \times \frac{20}{100} = 900
\displaystyle \therefore\ \text{Total annual income} = \text{Number of shares} \times \text{Nominal value of a share} \times \frac{\text{Rate of dividend}}{100}
\displaystyle \Rightarrow n = \frac{900}{10} = 90
\displaystyle (i)\ \text{Amount invested by Mr. Sharma} = 90 \times 80 = \text{Rs }7200
\displaystyle (ii)\ \text{Percentage return} = \frac{\text{Annual Income}}{\text{Amount Invested}} \times 100 = \frac{900}{7200}\times 100 = \frac{100}{8} = 12.5\%

Question 13: A man invests \displaystyle \text{Rs }22500 in \displaystyle \text{Rs }50 shares available at \displaystyle 10\% discount. If the dividend paid by the company is \displaystyle 12\%, calculate
(i) the number of shares purchased.
(ii) the annual dividend received.
(iii) the rate of return he gets on his investment. Give your answer correct to the nearest whole number.
[ICSE 2018]
\displaystyle \text{Answer:}
\displaystyle 4.\ \text{Issued price of each share} = 50 - \frac{10}{100}\times 50 = \text{Rs }45
\displaystyle \text{Total investment} = \text{Rs }22500
\displaystyle (i)\ \text{Number of shares purchased} = \frac{22500}{45} = 500
\displaystyle (ii)\ \text{Annual dividend} = \text{Number of shares purchased} \times \text{Face value of a share} \times \frac{12}{100}
\displaystyle = 500 \times 50 \times \frac{12}{100} = \text{Rs }3000
\displaystyle (iii)\ \text{Rate of return} = \frac{\text{Dividend}}{\text{Invested amount}} \times 100 = \frac{3000}{22500}\times 100 \approx 13\%

Question 14: How much should a man invest in \displaystyle \text{Rs }50 shares selling at \displaystyle \text{Rs }60 to obtain an income of \displaystyle \text{Rs }450, if the rate of dividend declared is \displaystyle 10\%? Also, find his yield percent, to the nearest whole number.     [ICSE 2017]
\displaystyle \text{Answer:}
\displaystyle 5.\ \text{Given, rate of dividend} = 10\%
\displaystyle \therefore\ \text{Dividend on 1 share of Rs }50 = \frac{10}{100}\times 50 = \text{Rs }5
\displaystyle \text{Number of shares bought} = \frac{\text{Total dividend}}{\text{Dividend on 1 share}} = \frac{450}{5} = 90
\displaystyle \text{Market value of 1 share} = \text{Rs }60
\displaystyle \text{Total investment} = 60 \times 90 = \text{Rs }5400
\displaystyle \text{Yield percent} = \frac{450}{5400}\times 100 = 8.33\% \approx 8\%

Question 15: Ashok invested \displaystyle \text{Rs }26400 on \displaystyle 12\%, \displaystyle \text{Rs }25 shares of a company. If he receives a dividend of \displaystyle \text{Rs }2475, then find
(i) number of shares he bought.
(ii) market value of each share.
[ICSE 2016]
\displaystyle \text{Answer:}
\displaystyle 6.\ \text{Total income} = \text{Rs }2475
\displaystyle \text{Annual income from 1 share} = \frac{12}{100}\times 25 = \text{Rs }3
\displaystyle (i)\ \text{Number of shares bought by Ashok} = \frac{2475}{3} = 825
\displaystyle (ii)\ \text{Market value of each share} = \frac{26400}{825} = \text{Rs }32

Question 16: Salman invests a sum of money in \displaystyle \text{Rs }50 shares, paying \displaystyle 15\% dividend quoted at \displaystyle 20\% premium. If his annual dividend is \displaystyle \text{Rs }600, calculate
(i) the number of shares he bought.
(ii) his total investment.
(iii) the rate of return on his investment.
[ICSE 2014]
\displaystyle \text{Answer:}
\displaystyle 7.\ \text{Nominal value of one share} = \text{Rs }50
\displaystyle \text{Dividend on one share} = \frac{15}{100}\times 50 = \text{Rs }7.50
\displaystyle \text{Total dividend received} = \text{Rs }600
\displaystyle (i)\ \text{Number of shares Salman bought} = \frac{600}{7.50} = 80
\displaystyle (ii)\ \text{Premium on one share} = \frac{20}{100}\times 50 = \text{Rs }10
\displaystyle \text{Market value of one share} = 50 + 10 = \text{Rs }60
\displaystyle \text{Total investment} = 80 \times 60 = \text{Rs }4800
\displaystyle (iii)\ \text{Rate of return} = \frac{600}{4800}\times 100 = 12.5\%

Question 17: A man invests \displaystyle \text{Rs }9600 on \displaystyle \text{Rs }100 shares at \displaystyle \text{Rs }80. If the company pays him \displaystyle 18\% dividend, find
(i) the number of shares he buys.
(ii) his total dividend.
(iii) his percentage return on the shares.
[ICSE 2012]
\displaystyle \text{Answer:}
\displaystyle 8.\ \text{Money invested} = \text{Rs }9600,\ \text{Nominal value} = \text{Rs }100,\ \text{Market value} = \text{Rs }80,\ \text{Rate of dividend} = 18\%
\displaystyle (i)\ \text{Number of shares} = \frac{9600}{80} = 120
\displaystyle (ii)\ \text{Total dividend} = 120 \times \frac{18}{100}\times 100 = \text{Rs }2160
\displaystyle (iii)\ \text{Return percentage} = \frac{2160}{9600}\times 100 = 22.5\%

Question 18: Mr. Prakash invested \displaystyle \text{Rs }52000 on \displaystyle \text{Rs }100 shares at a discount of \displaystyle \text{Rs }20 paying \displaystyle 8\% dividend. At the end of one year, he sells the shares at a premium of \displaystyle \text{Rs }20. Find
(i) the annual dividend.
(ii) the profit earned including his dividend.
[ICSE 2011]
\displaystyle \text{Answer:}
\displaystyle 9.\ \text{Money invested by Mr. Prakash} = \text{Rs }52000
\displaystyle \text{Nominal value of one share} = \text{Rs }100
\displaystyle \text{Market value of one share} = 100 - 20 = \text{Rs }80,\ \text{Dividend} = 8\%
\displaystyle \text{Number of shares} = \frac{52000}{80} = 650
\displaystyle (i)\ \text{Annual dividend} = \frac{8}{100}\times 650 \times 100 = \text{Rs }5200
\displaystyle (ii)\ \text{Selling price of one share} = 100 + 20 = \text{Rs }120
\displaystyle \text{Total selling price} = 650 \times 120 = \text{Rs }78000
\displaystyle \text{Profit} = (78000 + 5200 - 52000) = \text{Rs }31200

Question 19:  Amit Kumar invests \displaystyle \text{Rs }36000 in buying \displaystyle \text{Rs }100 shares at \displaystyle \text{Rs }20 premium. The dividend is \displaystyle 15\% per annum. Find
(i) the number of shares he buys.
(ii) his yearly dividend.
(iii) the percentage return on his investment.
Give your answer correct to the nearest whole number.
[ICSE 2009]
\displaystyle \text{Answer:}
\displaystyle 10.\ \text{Nominal value of a share} = \text{Rs }100,\ \text{Market value} = 100 + 20 = \text{Rs }120
\displaystyle \text{Money invested} = \text{Rs }36000,\ \text{Rate of dividend} = 15\%
\displaystyle (i)\ \text{Number of shares} = \frac{36000}{120} = 300
\displaystyle (ii)\ \text{Dividend on one share} = \frac{15}{100}\times 100 = \text{Rs }15
\displaystyle \text{Dividend on 300 shares} = 15 \times 300 = \text{Rs }4500
\displaystyle (iii)\ \text{Return percentage} = \frac{4500}{36000}\times 100 = 12.5\%

Question 20: Ajay owns 560 shares of a company. The face value of each share is \displaystyle \text{Rs }25. The company declares a dividend of \displaystyle 9\%. Calculate
(i) the dividend that Ajay will get.
(ii) the rate of interest on his investment, if Ajay had paid \displaystyle \text{Rs }30 for each share.
[ICSE 2007]
\displaystyle \text{Answer:}
\displaystyle 11.\ \text{Number of shares Ajay owns} = 560,\ \text{Face value} = \text{Rs }25,\ \text{Rate of dividend} = 9\%
\displaystyle \text{Dividend on one share} = \frac{9}{100}\times 25 = \text{Rs }\frac{9}{4}
\displaystyle (i)\ \text{Dividend on 560 shares} = \frac{9}{4}\times 560 = \text{Rs }1260
\displaystyle (ii)\ \text{Total investment} = 560 \times 30 = \text{Rs }16800
\displaystyle \text{Rate of interest} = \frac{1260}{16800}\times 100 = 7.5\%

Question 21: Mr. Tiwari invested \displaystyle \text{Rs }29040 in \displaystyle 15\%, \displaystyle \text{Rs }100 shares quoted at a premium of \displaystyle 20\%. Calculate
(i) the number of shares bought by Mr. Tiwari.
(ii) Mr. Tiwari’s income from the investment.
(iii) the percentage return on his investment.
[ICSE 2005]
\displaystyle \text{Answer:}
\displaystyle 12.\ \text{Given, money invested by Mr. Tiwari} = \text{Rs }29040,\ \text{Rate of dividend} = 15\%,\ \text{Nominal value of a share} = \text{Rs }100,\ \text{Rate of premium} = 20\%
\displaystyle (i)\ \text{Market value of one share} = 100 + \frac{20}{100}\times 100 = \text{Rs }120
\displaystyle \text{Number of shares} = \frac{29040}{120} = 242
\displaystyle (ii)\ \text{Mr. Tiwari's income} = 242 \times \frac{15}{100}\times 100 = \text{Rs }3630
\displaystyle (iii)\ \text{Percentage return} = \frac{3630}{29040}\times 100 = 12.5\%

Question 22: A man invests \displaystyle \text{Rs }8800 on buying shares of face value of \displaystyle \text{Rs }100 each at a premium of \displaystyle 10\% in a company. If he earns \displaystyle \text{Rs }1200 at the end of the year as dividend, find
(i) the number of shares he has in the company.
(ii) the dividend percentage per share.
[ICSE 2001]
\displaystyle \text{Answer:}
\displaystyle 13.\ \text{Given, money invested} = \text{Rs }8800,\ \text{Nominal value} = \text{Rs }100,\ \text{Rate of premium} = 10\%,\ \text{Dividend earned} = \text{Rs }1200
\displaystyle \text{Market value of a share} = 100 + \frac{10}{100}\times 100 = \text{Rs }110
\displaystyle (i)\ \text{Number of shares} = \frac{8800}{110} = 80
\displaystyle (ii)\ \text{Dividend percentage} = \frac{1200}{100 \times 80}\times 100 = 15\%

Question 23: A man bought 200 shares each of face value \displaystyle \text{Rs }10 at \displaystyle \text{Rs }12 per share. At the end of the year, the company from which he bought the shares declares a dividend of \displaystyle 15\%. Calculate
(i) the amount of money invested by the man.
(ii) the amount of dividend he received.
(iii) the percentage return on his outlay.
[ICSE 2017]
\displaystyle \text{Answer:}
\displaystyle 14.\ \text{Given, face value of one share} = \text{Rs }10,\ \text{Market value} = \text{Rs }12,\ \text{Number of shares} = 200,\ \text{Dividend} = 15\%
\displaystyle (i)\ \text{Money invested} = 200 \times 12 = \text{Rs }2400
\displaystyle (ii)\ \text{Total dividend} = 200 \times \frac{15}{100}\times 10 = \text{Rs }300
\displaystyle (iii)\ \text{Return percentage} = \frac{300}{2400}\times 100 = 12.5\%

Question 24: Rohit invested \displaystyle \text{Rs }9600 on \displaystyle \text{Rs }100 shares at \displaystyle \text{Rs }20 premium paying \displaystyle 8\% dividend. Rohit sold the shares when the price rose to \displaystyle \text{Rs }160. He invested the proceeds (excluding dividend) in \displaystyle 10\%, \displaystyle \text{Rs }50 shares at \displaystyle \text{Rs }40. Find
(i) original number of shares.
(ii) sale proceeds.
(iii) new number of shares.
(iv) change in the two dividends.
[ICSE 2015]
\displaystyle \text{Answer:}
\displaystyle 15.\ \text{Money invested by Rohit} = \text{Rs }9600
\displaystyle (i)\ \text{Original number of shares} = \frac{9600}{120} = 80
\displaystyle (ii)\ \text{Sale proceeds} = 80 \times 160 = \text{Rs }12800
\displaystyle (iii)\ \text{New number of shares} = \frac{12800}{40} = 320
\displaystyle (iv)\ \text{Change in dividends} = 10\% \times (320 \times 50) - 8\% \times (80 \times 100) = 1600 - 640 = \text{Rs }960

Question 25: Salman buys 50 shares of face value \displaystyle \text{Rs }100 available at \displaystyle \text{Rs }132.
(i) What is his investment?
(ii) If the dividend is \displaystyle 7.5\%, then what will be his annual income?
(iii) If he wants to increase his annual income by \displaystyle \text{Rs }150, then how many extra shares should he buy?
[ICSE 2013]
\displaystyle \text{Answer:}
\displaystyle 16.\ \text{Given, number of shares} = 50,\ \text{Face value} = \text{Rs }100,\ \text{Market value} = \text{Rs }132
\displaystyle (i)\ \text{Investment} = 132 \times 50 = \text{Rs }6600
\displaystyle (ii)\ \text{Annual income} = 50 \times \frac{7.5}{100}\times 100 = \text{Rs }375
\displaystyle (iii)\ \text{Let extra shares be }x,\ \text{Total shares} = 50 + x
\displaystyle \text{New income} = (50 + x)\times \frac{7.5}{100}\times 100 = (50 + x)\times 7.5
\displaystyle (50 + x)\times 7.5 = 375 + 150 = 525
\displaystyle 50 + x = \frac{525}{7.5} = 70 \Rightarrow x = 20
\displaystyle \Rightarrow 50 + x = 70
\displaystyle \Rightarrow x = 70 - 50
\displaystyle \Rightarrow x = 20
\displaystyle \therefore\ \text{Hence, the number of extra shares he buys, is }20.

Question 26: Vivek invests \displaystyle \text{Rs }4500 in \displaystyle 8\%, \displaystyle \text{Rs }10 shares at \displaystyle \text{Rs }15. He sells the shares when the price rises to \displaystyle \text{Rs }30 and invests the proceeds in \displaystyle 12\%, \displaystyle \text{Rs }100 shares at \displaystyle \text{Rs }125. Calculate
(i) the sale proceeds.
(ii) the number of \displaystyle \text{Rs }125 shares he buys.
(iii) the change in his annual income from dividend.
[ICSE 2010]
\displaystyle \text{Answer:}
\displaystyle 17.\ \text{Given, money invested by Vivek} = \text{Rs }4500
\displaystyle \text{Nominal value of a share} = \text{Rs }10
\displaystyle \text{Market value of one share} = \text{Rs }15
\displaystyle \text{Number of shares he bought} = \frac{\text{Money invested}}{\text{Market value of one share}} = \frac{4500}{15} = 300
\displaystyle (i)\ \text{Sale proceed} = \text{Amount received on selling 300 shares} = 300 \times 30 = \text{Rs }9000
\displaystyle (ii)\ \text{He bought a share at Rs }125,\ \text{therefore number of shares he bought} = \frac{9000}{125} = 72
\displaystyle (iii)\ \text{Change in annual income} = 12\% \text{ of }(72 \times 100) - 8\% \text{ of }(300 \times 10)
\displaystyle = 864 - 240 = \text{Rs }624

Question 27: A company with 4000 shares of nominal value of \displaystyle \text{Rs }110 each declares an annual dividend of \displaystyle 15\%. Calculate
(i) the total amount of dividend paid by the company.
(ii) the annual income of Shahrukh, who holds 88 shares in the company.
(iii) if he received only \displaystyle 10\% on his investment, find the price Shahrukh paid for each share.
[ICSE 2008]
\displaystyle \text{Answer:}
\displaystyle 18.\ \text{Given, the number of shares} = 4000,\ \text{Nominal value of a share} = \text{Rs }110,\ \text{Rate of dividend} = 15\%
\displaystyle (i)\ \text{Dividend on one share} = 110 \times 15\% = 110 \times \frac{15}{100} = \text{Rs }16.50
\displaystyle \text{Total dividend} = 4000 \times 16.50 = \text{Rs }66000
\displaystyle (ii)\ \text{Annual income of Shahrukh on 88 shares} = 88 \times 16.50 = \text{Rs }1452
\displaystyle (iii)\ \text{Let Shahrukh's investment be }x.
\displaystyle \text{According to the question, }10\% \text{ of money invested} = \text{Annual income of Shahrukh}
\displaystyle \Rightarrow 10\% \times x = 1452
\displaystyle \Rightarrow \frac{10x}{100} = 1452 \Rightarrow x = 1452 \times 10
\displaystyle \Rightarrow x = 14520
\displaystyle \therefore\ \text{The price Shahrukh paid for each share} = \frac{14520}{88} = \text{Rs }165

Question 28: Mr. Ram Gopal invested \displaystyle \text{Rs }8000 in \displaystyle 7\%, \displaystyle \text{Rs }100 shares at \displaystyle \text{Rs }80. After a year, he sold these shares at \displaystyle \text{Rs }75 each and invested the proceeds in \displaystyle 18\% at \displaystyle \text{Rs }25 shares at \displaystyle \text{Rs }41. Find
(i) his dividend for the first year.
(ii) his annual income from the second investment.
(iii) the percentage of increase in return on his original investment.
[ICSE 2006]
\displaystyle \text{Answer:}
\displaystyle 19.\ \text{Given, money invested by Mr. Ram Gopal} = \text{Rs }8000
\displaystyle \text{Market value of one share} = \text{Rs }80,\ \text{Rate of dividend} = 7\%
\displaystyle (i)\ \text{Number of shares he buys} = \frac{8000}{80} = 100
\displaystyle \text{Dividend on one share} = 7\% \text{ of Rs }100 = \frac{7}{100}\times 100 = \text{Rs }7
\displaystyle \therefore\ \text{Dividend for the first year} = 100 \times 7 = \text{Rs }700
\displaystyle \text{Given, selling price of one share} = \text{Rs }75
\displaystyle \text{Selling price of 100 shares} = 100 \times 75 = \text{Rs }7500
\displaystyle \text{Total amount received} = 7500 + 700 = \text{Rs }8200
\displaystyle \text{Now, further investment} = \text{Rs }8200
\displaystyle \text{Market value} = \text{Rs }41,\ \text{Nominal value} = \text{Rs }25,\ \text{Rate of dividend} = 18\%
\displaystyle \text{Number of shares bought} = \frac{8200}{41} = 200
\displaystyle \text{Total nominal value} = 200 \times 25 = 5000
\displaystyle \text{Dividend received} = 18\% \text{ of }5000 = \frac{18}{100}\times 5000 = \text{Rs }900
\displaystyle \therefore\ \text{Annual income in second year} = \text{Rs }900
\displaystyle (iii)\ \text{Increase in return} = 900 - 700 = \text{Rs }200
\displaystyle \text{Percentage increase in return} = \frac{200}{8000}\times 100 = 2.5\%

Question 29: A man invested \displaystyle \text{Rs }45000 in \displaystyle 15\%, \displaystyle \text{Rs }100 shares quoted at \displaystyle \text{Rs }125. When the market value of these shares rose to \displaystyle \text{Rs }140, he sold some shares, just enough to raise \displaystyle \text{Rs }8400. Calculate
(i) the number of shares he still holds.
(ii) the dividend due to him on these remaining shares.
[ICSE 2004]
\displaystyle \text{Answer:}
\displaystyle 20.\ \text{Given, money invested} = \text{Rs }45000,\ \text{Rate of dividend} = 15\%
\displaystyle \text{Nominal value of a share} = \text{Rs }100,\ \text{Market value of a share} = \text{Rs }125
\displaystyle \text{Number of shares bought} = \frac{45000}{125} = 360
\displaystyle \text{When market value rose to Rs }140,\ \text{amount raised} = \text{Rs }8400
\displaystyle \text{Shares sold} = \frac{8400}{140} = 60
\displaystyle (i)\ \text{Shares still held} = 360 - 60 = 300
\displaystyle (ii)\ \text{Dividend on remaining shares} = 15\% \text{ of }(300 \times 100) = \frac{15}{100}\times 300 \times 100 = \text{Rs }4500

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