Class 10: Shares and Dividend

$\displaystyle \textbf{Question 1: } \text{A man buys }75,\ \text{Rs. }100\text{ shares paying }9\%\text{ dividend.}$
$\displaystyle \text{He buys the shares at such a price that he gets }12\%\text{ on his investment.}$
$\displaystyle \text{At what price did he buy the shares?}$
$\displaystyle \text{Answer:}$
$\displaystyle \text{Nominal value of one share}=\text{Rs. }100$
$\displaystyle \text{Let the market price of one share}=(100+x)\text{ Rs.}$
$\displaystyle \text{Annual dividend}=75\times100\times\frac{9}{100}=\text{Rs. }675$
$\displaystyle \frac{12}{100}\times75(100+x)=675$
$\displaystyle 9(100+x)=675$
$\displaystyle 900+9x=675$
$\displaystyle 9x=-225$
$\displaystyle x=-25$
$\displaystyle \therefore \text{Market price of one share}=100-25=\text{Rs. }75$
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$\displaystyle \textbf{Question 2: } \text{By purchasing Rs. }25\text{ gas shares for Rs. }40\text{ each, a man}$
$\displaystyle \text{gets }4\%\text{ profit on his investment. What rate per cent is the company}$
$\displaystyle \text{paying? What is his dividend if he buys }60\text{ shares?}$
$\displaystyle \text{Answer:}$
$\displaystyle \text{Nominal value of one share}=\text{Rs. }25$
$\displaystyle \text{Market price of one share}=\text{Rs. }40$
$\displaystyle \text{Let the dividend rate be }x\%$
$\displaystyle 60\times25\times\frac{x}{100}=60\times40\times\frac{4}{100}$
$\displaystyle 25x=160$
$\displaystyle x=6.4\%$
$\displaystyle \text{Dividend on }60\text{ shares}=60\times25\times\frac{6.4}{100}=\text{Rs. }96$
$\displaystyle \therefore \text{Dividend rate}=6.4\%\text{ and annual dividend}=\text{Rs. }96$
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$\displaystyle \textbf{Question 3: } \text{Rs. }100\text{ shares of a company are available in the market}$
$\displaystyle \text{at a premium of Rs. }20.\text{ Find the rate of dividend given by the company,}$
$\displaystyle \text{when a man's return on his investment is }15\%.\$
$\displaystyle \text{Answer:}$
$\displaystyle \text{Nominal value of one share}=\text{Rs. }100$
$\displaystyle \text{Market price of one share}=100+20=\text{Rs. }120$
$\displaystyle \text{Let the rate of dividend be }x\%.$
$\displaystyle \text{Dividend on one share}=100\times\frac{x}{100}=\text{Rs. }x$
$\displaystyle \text{Return on investment on one share}=120\times\frac{15}{100}=\text{Rs. }18$
$\displaystyle \therefore x=18$
$\displaystyle \therefore \text{Rate of dividend}=18\%$
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$\displaystyle \textbf{Question 4: } \text{Rs. }50\text{ shares of a company are quoted at a discount of }10\%.$
$\displaystyle \text{Find the rate of dividend given by the company, the return on investment}$
$\displaystyle \text{on these shares being }20\%.\$
$\displaystyle \text{Answer:}$
$\displaystyle \text{Let the nominal value of one share}=\text{Rs. }x$
$\displaystyle \text{Market price of one share}=x-10\%\text{ of }x=0.9x\text{ Rs.}$
$\displaystyle \text{Let the rate of dividend be }y\%.$
$\displaystyle x\times\frac{y}{100}=0.9x\times\frac{20}{100}$
$\displaystyle y=18$
$\displaystyle \therefore \text{Rate of dividend}=18\%$
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$\displaystyle \textbf{Question 5: } \text{A company declares an }8\%\text{ dividend to the shareholders.}$
$\displaystyle \text{If a man receives Rs. }2840\text{ as his dividend, find the nominal value}$
$\displaystyle \text{of his shares.}$
$\displaystyle \text{Answer:}$
$\displaystyle \text{Let the nominal value of his shares}=\text{Rs. }x$
$\displaystyle x\times\frac{8}{100}=2840$
$\displaystyle x=\frac{2840\times100}{8}=\text{Rs. }35500$
$\displaystyle \therefore \text{Nominal value of his shares}=\text{Rs. }35500$
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$\displaystyle \textbf{Question 6: } \text{How much should a man invest in Rs. }100\text{ shares selling at}$
$\displaystyle \text{Rs. }110\text{ to obtain an annual income of Rs. }1680,\text{ if the dividend}$
$\displaystyle \text{declared is }12\%\text{?}$
$\displaystyle \text{Answer:}$
$\displaystyle \text{Nominal value of one share}=\text{Rs. }100$
$\displaystyle \text{Market price of one share}=\text{Rs. }110$
$\displaystyle \text{Let the number of shares bought}=x$
$\displaystyle x\times100\times\frac{12}{100}=1680$
$\displaystyle 12x=1680$
$\displaystyle x=140$
$\displaystyle \therefore \text{Amount invested}=140\times110=\text{Rs. }15400$
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$\displaystyle \textbf{Question 7: } \text{A company declares a dividend of }11.2\%\text{ to all its}$
$\displaystyle \text{shareholders. If its Rs. }60\text{ share is available in the market at a}$
$\displaystyle \text{premium of }25\%,\text{ how much should a person invest to have an}$
$\displaystyle \text{annual income of Rs. }1680\text{?}$
$\displaystyle \text{Answer:}$
$\displaystyle \text{Nominal value of one share}=\text{Rs. }60$
$\displaystyle \text{Market price of one share}=60+25\%\text{ of }60=\text{Rs. }75$
$\displaystyle \text{Let the number of shares bought}=x$
$\displaystyle x\times60\times\frac{11.2}{100}=1680$
$\displaystyle 6.72x=1680$
$\displaystyle x=250$
$\displaystyle \therefore \text{Amount invested}=250\times75=\text{Rs. }18750$
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$\displaystyle \textbf{Question 8: } \text{A man buys }400,\ \text{Rs. }20\text{ shares at a premium of}$
$\displaystyle \text{Rs. }4\text{ each and receives a dividend of }12\%.\text{ Find:}$
$\displaystyle \text{(i) The amount invested \quad (ii) His total income from the shares}$
$\displaystyle \text{(iii) Percentage return on his money.}$
$\displaystyle \text{Answer:}$
$\displaystyle \text{Nominal value of one share}=\text{Rs. }20$
$\displaystyle \text{Market price of one share}=20+4=\text{Rs. }24$
$\displaystyle \text{Number of shares bought}=400$
$\displaystyle \text{Amount invested}=400\times24=\text{Rs. }9600$
$\displaystyle \text{Annual income}=400\times20\times\frac{12}{100}=\text{Rs. }960$
$\displaystyle \text{Percentage return}=\frac{960}{9600}\times100=10\%$
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$\displaystyle \textbf{Question 9: } \text{A man buys }400,\ \text{Rs. }20\text{ shares at a discount of }20\%$
$\displaystyle \text{and receives a return of }12\%\text{ on his money. Calculate:}$
$\displaystyle \text{(i) The amount invested \qquad (ii) The rate of dividend paid by the company.}$
$\displaystyle \text{Answer:}$
$\displaystyle \text{Nominal value of one share}=\text{Rs. }20$
$\displaystyle \text{Market price of one share}=20-20\%\text{ of }20=\text{Rs. }16$
$\displaystyle \text{Number of shares bought}=400$
$\displaystyle \text{Amount invested}=400\times16=\text{Rs. }6400$
$\displaystyle \text{Return on investment}=\frac{12}{100}\times6400=\text{Rs. }768$
$\displaystyle \text{Let the rate of dividend be }x\%$
$\displaystyle 400\times20\times\frac{x}{100}=768$
$\displaystyle 80x=768$
$\displaystyle x=9.6$
$\displaystyle \therefore \text{Rate of dividend}=9.6\%$
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$\displaystyle \textbf{Question 10: } \text{A company, with }10000\text{ shares of Rs. }100\text{ each, declares}$
$\displaystyle \text{an annual dividend of }5\%.\text{ (i) What is the total amount of dividend}$
$\displaystyle \text{paid by the company? (ii) What should be the annual income of a man who}$
$\displaystyle \text{has }72\text{ shares in the company? (iii) If he received only }4\%\text{ of his}$
$\displaystyle \text{investment, find the price he paid for each share.}$
$\displaystyle \text{Answer:}$
$\displaystyle \text{Total dividend paid}=10000\times100\times\frac{5}{100}=\text{Rs. }50000$
$\displaystyle \text{Annual income of the man}=72\times100\times\frac{5}{100}=\text{Rs. }360$
$\displaystyle \text{Let the market price of one share be Rs. }x$
$\displaystyle \text{Total investment}=72x$
$\displaystyle 72x\times\frac{4}{100}=360$
$\displaystyle x=125$
$\displaystyle \therefore \text{Price paid for each share}=\text{Rs. }125$
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$\displaystyle \textbf{Question 11: } \text{A lady holds }1800,\ \text{Rs. }100\text{ shares of a company that}$
$\displaystyle \text{pays a }15\%\text{ dividend annually. Calculate her annual dividend. If she}$
$\displaystyle \text{had bought these shares at a }40\%\text{ premium, what is the return she}$
$\displaystyle \text{gets as a per cent on her investment? Give your answer to the nearest integer.}$
$\displaystyle \text{Answer:}$
$\displaystyle \text{Annual dividend}=1800\times100\times\frac{15}{100}=\text{Rs. }27000$
$\displaystyle \text{Investment}=1800\times140=\text{Rs. }252000$
$\displaystyle \text{Return}\%=\frac{27000}{252000}\times100=10.71\%$
$\displaystyle \therefore \text{Return on investment}\approx11\%\text{ (nearest integer)}$
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$\displaystyle \textbf{Question 12: } \text{A man invests Rs. }11200\text{ in a company paying }6\%\text{ per annum}$
$\displaystyle \text{when its Rs. }100\text{ shares can be bought for Rs. }140.\text{ Find:}$
$\displaystyle \text{(i) His annual dividend \qquad (ii) His percentage return on his investment.}$
$\displaystyle \text{Answer:}$
$\displaystyle \text{Number of shares bought}=\frac{11200}{140}=80$
$\displaystyle \text{Annual dividend}=80\times100\times\frac{6}{100}=\text{Rs. }480$
$\displaystyle \text{Percentage return}=\frac{480}{11200}\times100=4.29\%$
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$\displaystyle \textbf{Question 13: } \text{A person has }60\text{ shares of nominal value Rs. }100\text{ and sells them}$
$\displaystyle \text{when they are at a premium of }60\%.\text{ He invests the proceeds in shares}$
$\displaystyle \text{of nominal value Rs. }50,\text{ quoted at }4\%\text{ discount and paying }18\%$
$\displaystyle \text{dividend annually. Calculate: (i) The sale proceeds (ii) The number of shares}$
$\displaystyle \text{he buys and (iii) His annual dividend from the shares.}$
$\displaystyle \text{Answer:}$
$\displaystyle \text{Selling price of one old share}=100+60\%\text{ of }100=\text{Rs. }160$
$\displaystyle \text{Sale proceeds}=60\times160=\text{Rs. }9600$
$\displaystyle \text{Market price of one new share}=50-4\%\text{ of }50=\text{Rs. }48$
$\displaystyle \text{Number of new shares bought}=\frac{9600}{48}=200$
$\displaystyle \text{Annual dividend}=200\times50\times\frac{18}{100}=\text{Rs. }1800$
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$\displaystyle \textbf{Question 14: } \text{A company with }10000\text{ shares of nominal value Rs. }100\text{ declares}$
$\displaystyle \text{an annual dividend of }8\%\text{ to the shareholders. (i) Calculate the total}$
$\displaystyle \text{amount of dividend paid by the company. (ii) A man had bought }90\text{ shares}$
$\displaystyle \text{of the company at Rs. }150\text{ per share. Calculate the dividend he receives}$
$\displaystyle \text{and the percentage return on his investment.}$
$\displaystyle \text{Answer:}$
$\displaystyle \text{Total dividend paid}=10000\times100\times\frac{8}{100}=\text{Rs. }80000$
$\displaystyle \text{Dividend received by the man}=90\times100\times\frac{8}{100}=\text{Rs. }720$
$\displaystyle \text{Investment}=90\times150=\text{Rs. }13500$
$\displaystyle \text{Percentage return}=\frac{720}{13500}\times100=5.33\%$
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$\displaystyle \textbf{Question 15: } \text{Which is the better investment: }16\%\text{ Rs. }100\text{ shares at }80$
$\displaystyle \text{or }20\%\text{ Rs. }100\text{ shares at }120\text{?}$
$\displaystyle \text{Answer:}$
$\displaystyle \text{For }16\%\text{ Rs. }100\text{ shares at Rs. }80:$
$\displaystyle \text{Dividend on }100\text{ shares}=100\times100\times\frac{16}{100}=\text{Rs. }1600$
$\displaystyle \text{Investment}=100\times80=\text{Rs. }8000$
$\displaystyle \text{Percentage return}=\frac{1600}{8000}\times100=20\%$
$\displaystyle \text{For }20\%\text{ Rs. }100\text{ shares at Rs. }120:$
$\displaystyle \text{Dividend on }100\text{ shares}=100\times100\times\frac{20}{100}=\text{Rs. }2000$
$\displaystyle \text{Investment}=100\times120=\text{Rs. }12000$
$\displaystyle \text{Percentage return}=\frac{2000}{12000}\times100=16.67\%$
$\displaystyle \therefore \text{The first investment gives a better return.}$
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$\displaystyle \textbf{Question 16: } \text{A man has a choice to invest in }200\text{ Rs. shares of two firms}$
$\displaystyle \text{at Rs. }120\text{ or Rs. }132.\text{ The first firm pays }5\%\text{ dividend and the}$
$\displaystyle \text{second firm pays }6\%\text{ dividend. Find: (i) Which company gives a better}$
$\displaystyle \text{return? (ii) If a man invests Rs. }26400\text{ with each firm, find the}$
$\displaystyle \text{difference between the annual returns.}$
$\displaystyle \text{Answer:}$
$\displaystyle \text{First company:}$
$\displaystyle \text{Dividend on }100\text{ shares}=100\times200\times\frac{5}{100}=\text{Rs. }1000$
$\displaystyle \text{Investment in }100\text{ shares}=100\times120=\text{Rs. }12000$
$\displaystyle \text{Percentage return}=\frac{1000}{12000}\times100=8.33\%$
$\displaystyle \text{Annual return on Rs. }26400=\frac{26400}{120}\times200\times\frac{5}{100}=\text{Rs. }2200$
$\displaystyle \text{Second company:}$
$\displaystyle \text{Dividend on }100\text{ shares}=100\times200\times\frac{6}{100}=\text{Rs. }1200$
$\displaystyle \text{Investment in }100\text{ shares}=100\times132=\text{Rs. }13200$
$\displaystyle \text{Percentage return}=\frac{1200}{13200}\times100=9.09\%$
$\displaystyle \text{Annual return on Rs. }26400=\frac{26400}{132}\times200\times\frac{6}{100}=\text{Rs. }2400$
$\displaystyle \therefore \text{The second company gives the better return.}$
$\displaystyle \text{Difference between the annual returns}=2400-2200=\text{Rs. }200$
$\\$

$\displaystyle \textbf{Question 17: } \text{A man bought }360,\ \text{Rs. }10\text{ shares of a company paying}$
$\displaystyle 12\%\text{ per annum. He sold the shares when their price rose to Rs. }21\text{ each}$
$\displaystyle \text{and invested the proceeds in Rs. }5\text{ shares paying }4.5\%\text{ per annum}$
$\displaystyle \text{at Rs. }3.50\text{ per share. Find the annual change in his income.}$
$\displaystyle \text{Answer:}$
$\displaystyle \text{Annual income from first investment}=360\times10\times\frac{12}{100}=\text{Rs. }432$
$\displaystyle \text{Sale proceeds}=360\times21=\text{Rs. }7560$
$\displaystyle \text{Number of new shares bought}=\frac{7560}{3.50}=2160$
$\displaystyle \text{Annual income from second investment}=2160\times5\times\frac{4.5}{100}=\text{Rs. }486$
$\displaystyle \therefore \text{Annual increase in income}=486-432=\text{Rs. }54$
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$\displaystyle \textbf{Question 18: } \text{A man sold }400\text{ (Rs. }20\text{) shares of a company paying }5\%$
$\displaystyle \text{at Rs. }18,\text{ and invested the proceeds in (Rs. }10\text{) shares of another}$
$\displaystyle \text{company paying }7\%\text{ at Rs. }12.\text{ How many Rs. }10\text{ shares did he buy}$
$\displaystyle \text{and what was the change in his income?}$
$\displaystyle \text{Answer:}$
$\displaystyle \text{Annual income from first investment}=400\times20\times\frac{5}{100}=\text{Rs. }400$
$\displaystyle \text{Sale proceeds}=400\times18=\text{Rs. }7200$
$\displaystyle \text{Number of Rs. }10\text{ shares bought}=\frac{7200}{12}=600$
$\displaystyle \text{Annual income from second investment}=600\times10\times\frac{7}{100}=\text{Rs. }420$
$\displaystyle \therefore \text{Number of shares bought}=600$
$\displaystyle \therefore \text{Increase in annual income}=420-400=\text{Rs. }20$
$\\$

$\displaystyle \textbf{Question 19: } \text{Two brothers A and B invest Rs. }16000\text{ each in buying}$
$\displaystyle \text{shares of two companies. A buys }3\%\text{ Rs. }100\text{ shares at Rs. }80\text{ and B}$
$\displaystyle \text{buys Rs. }10\text{ shares at par. If they both receive equal dividends, find}$
$\displaystyle \text{the rate per cent of dividend received by B.}$
$\displaystyle \text{Answer:}$
$\displaystyle \text{Dividend received by A}=\frac{16000}{80}\times100\times\frac{3}{100}=\text{Rs. }600$
$\displaystyle \text{Hence dividend received by B}=\text{Rs. }600$
$\displaystyle \frac{16000}{10}\times10\times\frac{x}{100}=600$
$\displaystyle 16x=600$
$\displaystyle x=37.5$
$\displaystyle \therefore \text{Rate of dividend received by B}=3.75\%$
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$\displaystyle \textbf{Question 20: } \text{A man invests Rs. }20020\text{ in buying shares of N.V. Rs. }26$
$\displaystyle \text{at }10\%\text{ premium. The dividend on the shares is }15\%\text{ per annum. Calculate:}$
$\displaystyle \text{(i) The number of shares he buys \quad (ii) The dividend he receives annually}$
$\displaystyle \text{(iii) The rate of interest he gets on his money. }\text{[ICSE 2012]}$
$\displaystyle \text{Answer:}$
$\displaystyle \text{Market price of one share}=26+10\%\text{ of }26=26+2.60=\text{Rs. }28.60$
$\displaystyle \text{Number of shares bought}=\frac{20020}{28.60}=700$
$\displaystyle \text{Annual dividend}=700\times26\times\frac{15}{100}=\text{Rs. }2730$
$\displaystyle \text{Rate of interest}=\frac{2730}{20020}\times100=13.64\%$
$\\$

$\displaystyle \textbf{Question 21: } \text{A person invested Rs. }19200\text{ in }15\%\text{ Rs. }100\text{ shares}$
$\displaystyle \text{at }20\%\text{ discount. After a year she sold these shares at Rs. }90\text{ each}$
$\displaystyle \text{and invested the proceeds, including her dividend, in }20\%\text{ Rs. }50\text{ shares}$
$\displaystyle \text{at Rs. }42.\text{ Find: (i) The number of shares she buys \quad (ii) The dividend}$
$\displaystyle \text{she receives annually \quad (iii) The rate of interest she gets on her money.}$
$\displaystyle \text{Answer:}$
$\displaystyle \text{First investment:}$
$\displaystyle \text{Market price of one Rs. }100\text{ share}=100-20\%\text{ of }100=\text{Rs. }80$
$\displaystyle \text{Number of shares bought}=\frac{19200}{80}=240$
$\displaystyle \text{Dividend received}=240\times100\times\frac{15}{100}=\text{Rs. }3600$
$\displaystyle \text{Sale proceeds}=240\times90=\text{Rs. }21600$
$\displaystyle \text{Amount available for second investment}=21600+3600=\text{Rs. }25200$
$\displaystyle \text{Second investment:}$
$\displaystyle \text{Number of Rs. }50\text{ shares bought}=\frac{25200}{42}=600$
$\displaystyle \text{Annual dividend}=600\times50\times\frac{20}{100}=\text{Rs. }6000$
$\displaystyle \text{Rate of interest}=\frac{6000}{25200}\times100=23.81\%$
$\\$

$\displaystyle \textbf{Question 22: } \text{A person invested Rs. }19200\text{ in }15\%\text{ Rs. }100\text{ shares}$
$\displaystyle \text{at }20\%\text{ premium. After a year she sold these shares at Rs. }140\text{ each}$
$\displaystyle \text{and invested the proceeds (including her dividend) in }20\%\text{ Rs. }20\text{ shares}$
$\displaystyle \text{at Rs. }16.\text{ Find: (i) Dividend for the first year (ii) Annual income in the}$
$\displaystyle \text{second year (iii) Percentage change in the return on her original investment.}$
$\displaystyle \text{Answer:}$
$\displaystyle \text{First investment:}$
$\displaystyle \text{Market price of one share}=100+20\%\text{ of }100=\text{Rs. }120$
$\displaystyle \text{Number of shares bought}=\frac{19200}{120}=160$
$\displaystyle \text{Dividend for the first year}=160\times100\times\frac{15}{100}=\text{Rs. }2400$
$\displaystyle \text{Return on original investment}=\frac{2400}{19200}\times100=12.5\%$
$\displaystyle \text{Second investment:}$
$\displaystyle \text{Amount available}=160\times140+2400=\text{Rs. }24800$
$\displaystyle \text{Number of shares bought}=\frac{24800}{16}=1550$
$\displaystyle \text{Annual income in the second year}=1550\times20\times\frac{20}{100}=\text{Rs. }6200$
$\displaystyle \text{Return on original investment}=\frac{6200}{19200}\times100=32.29\%$
$\displaystyle \text{Percentage change in return}=32.29\%-12.5\%=19.79\%$
$\displaystyle \therefore \text{(i) Dividend for first year}=\text{Rs. }2400,\ \text{(ii) Annual income}=\text{Rs. }6200,$
$\displaystyle \text{(iii) Percentage increase in return on the original investment}=19.79\%$
$\\$