Class 10: Shares and Dividend

$\displaystyle \textbf{Question 1: } \text{How much money will be required to buy }200,\ \text{Rs. }25\text{ shares}$
$\displaystyle \text{at a premium of Rs. }2\text{?}$
$\displaystyle \text{Answer:}$
$\displaystyle \text{Market price of one share}=25+2=\text{Rs. }27$
$\displaystyle \therefore \text{Money required to buy }200\text{ shares}=200\times27=\text{Rs. }5400$
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$\displaystyle \textbf{Question 2: } \text{How much money will be required to buy }125,\ \text{Rs. }30\text{ shares}$
$\displaystyle \text{at a discount of Rs. }3\text{?}$
$\displaystyle \text{Answer:}$
$\displaystyle \text{Market price of one share}=30-3=\text{Rs. }27$
$\displaystyle \therefore \text{Money required to buy }125\text{ shares}=125\times27=\text{Rs. }3375$
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$\displaystyle \textbf{Question 3: } \text{A person buys }120\text{ shares at a nominal value of Rs. }40\text{ each,}$
$\displaystyle \text{which he sells at Rs. }42.50\text{ each. Find his profit and profit per cent.}$
$\displaystyle \text{Answer:}$
$\displaystyle \text{Profit per share}=42.50-40=\text{Rs. }2.50$
$\displaystyle \text{Total investment}=120\times40=\text{Rs. }4800$
$\displaystyle \text{Total profit}=120\times2.50=\text{Rs. }300$
$\displaystyle \text{Profit}\%=\frac{300}{4800}\times100=6\%$
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$\displaystyle \textbf{Question 4: } \text{Find the cost of }85,\ \text{Rs. }60\text{ shares when quoted at Rs. }63.25.$
$\displaystyle \text{Answer:}$
$\displaystyle \text{Cost of }85\text{ shares}=85\times63.25=\text{Rs. }5376.25$
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$\displaystyle \textbf{Question 5: } \text{A man invests Rs. }800\text{ in buying Rs. }5\text{ shares and when they are}$
$\displaystyle \text{selling at a premium of Rs. }1.15,\text{ he sells all the shares. Find his profit}$
$\displaystyle \text{and profit per cent.}$
$\displaystyle \text{Answer:}$
$\displaystyle \text{Number of shares bought}=\frac{800}{5}=160$
$\displaystyle \text{Selling price per share}=5+1.15=\text{Rs. }6.15$
$\displaystyle \text{Profit per share}=6.15-5=\text{Rs. }1.15$
$\displaystyle \text{Total investment}=\text{Rs. }800$
$\displaystyle \text{Total profit}=160\times1.15=\text{Rs. }184$
$\displaystyle \text{Profit}\%=\frac{184}{800}\times100=23\%$
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$\displaystyle \textbf{Question 6: } \text{Find the annual income derived from }250,\ \text{Rs. }60\text{ shares}$
$\displaystyle \text{paying }5\%\text{ dividend.}$
$\displaystyle \text{Answer:}$
$\displaystyle \text{Dividend per share}=60\times\frac{5}{100}=\text{Rs. }3$
$\displaystyle \therefore \text{Annual income}=250\times3=\text{Rs. }750$
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$\displaystyle \textbf{Question 7: } \text{A man invests Rs. }3072\text{ in a company paying }5\%\text{ per annum,}$
$\displaystyle \text{when its Rs. }10\text{ share can be bought for Rs. }16\text{ each. Find:}$
$\displaystyle \text{(i) His annual income \qquad (ii) His percentage income on his investment.}$
$\displaystyle \text{Answer:}$
$\displaystyle \text{Market price of one share}=\text{Rs. }16$
$\displaystyle \text{Number of shares bought}=\frac{3072}{16}=192$
$\displaystyle \text{Annual income}=192\times10\times\frac{5}{100}=\text{Rs. }96$
$\displaystyle \text{Percentage income}=\frac{96}{3072}\times100=3.125\%$
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$\displaystyle \textbf{Question 8: } \text{A man invests Rs. }7770\text{ in a company paying }5\%\text{ dividend}$
$\displaystyle \text{when a share of nominal value Rs. }100\text{ sells at a premium of Rs. }5.$
$\displaystyle \text{Find: (i) The number of shares bought \quad (ii) Percentage income}$
$\displaystyle \text{(iii) Annual income.}$
$\displaystyle \text{Answer:}$
$\displaystyle \text{Nominal value of one share}=\text{Rs. }100$
$\displaystyle \text{Market price of one share}=100+5=\text{Rs. }105$
$\displaystyle \text{Number of shares bought}=\frac{7770}{105}=74$
$\displaystyle \text{Annual income}=74\times100\times\frac{5}{100}=\text{Rs. }370$
$\displaystyle \text{Percentage income}=\frac{370}{7770}\times100\approx4.76\%$
$\displaystyle \therefore \text{(i) Number of shares}=74,\ \text{(ii) Percentage income}=4.76\%,\ \text{(iii) Annual income}=\text{Rs. }370$
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$\displaystyle \textbf{Question 9: } \text{A man buys Rs. }50\text{ shares of a company paying }12\%\text{ dividend}$
$\displaystyle \text{at a premium of Rs. }10.\text{ Find: (i) The market value of }320\text{ shares}$
$\displaystyle \text{(ii) His annual income \qquad (iii) His profit per cent.}$
$\displaystyle \text{Answer:}$
$\displaystyle \text{Nominal value of one share}=\text{Rs. }50$
$\displaystyle \text{Market price of one share}=50+10=\text{Rs. }60$
$\displaystyle \text{Market value of }320\text{ shares}=320\times60=\text{Rs. }19200$
$\displaystyle \text{Annual income}=320\times50\times\frac{12}{100}=\text{Rs. }1920$
$\displaystyle \text{Profit}\%=\frac{1920}{19200}\times100=10\%$
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$\displaystyle \textbf{Question 10: } \text{A man buys Rs. }75\text{ shares at a discount of Rs. }15\text{ of a company}$
$\displaystyle \text{paying }20\%\text{ dividend. Find: (i) The market value of }120\text{ shares}$
$\displaystyle \text{(ii) His annual income \qquad (iii) His profit per cent.}$
$\displaystyle \text{Answer:}$
$\displaystyle \text{Nominal value of one share}=\text{Rs. }75$
$\displaystyle \text{Market price of one share}=75-15=\text{Rs. }60$
$\displaystyle \text{Market value of }120\text{ shares}=120\times60=\text{Rs. }7200$
$\displaystyle \text{Annual income}=120\times75\times\frac{20}{100}=\text{Rs. }1800$
$\displaystyle \text{Profit}\%=\frac{1800}{7200}\times100=25\%$
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$\displaystyle \textbf{Question 11: } \text{A man has }300,\ \text{Rs. }50\text{ shares of a company paying}$
$\displaystyle 20\%\text{ dividend. Find his net income after paying }3\%\text{ income tax.}$
$\displaystyle \text{Answer:}$
$\displaystyle \text{Annual income}=300\times50\times\frac{20}{100}=\text{Rs. }3000$
$\displaystyle \text{Income tax}=\frac{3}{100}\times3000=\text{Rs. }90$
$\displaystyle \therefore \text{Net income}=3000-90=\text{Rs. }2910$
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$\displaystyle \textbf{Question 12: } \text{A company pays a dividend of }15\%\text{ on its Rs. }10\text{ shares}$
$\displaystyle \text{from which it deducts income tax at the rate of }22\%.\text{ Find the annual income}$
$\displaystyle \text{of a man who owns one thousand shares of this company.}$
$\displaystyle \text{Answer:}$
$\displaystyle \text{Gross annual income}=1000\times10\times\frac{15}{100}=\text{Rs. }1500$
$\displaystyle \text{Income tax deducted}=\frac{22}{100}\times1500=\text{Rs. }330$
$\displaystyle \therefore \text{Net annual income}=1500-330=\text{Rs. }1170$
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$\displaystyle \textbf{Question 13: } \text{A man invests Rs. }8800\text{ in buying shares of a company}$
$\displaystyle \text{of face value Rs. }100\text{ each at a premium of }10\%.\text{ If he earns Rs. }1200$
$\displaystyle \text{at the end of the year as dividend. Find: (i) The number of shares}$
$\displaystyle \text{he has in the company. (ii) The dividend per cent per share. }\text{[ICSE 2001]}$
$\displaystyle \text{Answer:}$
$\displaystyle \text{Face value of one share}=\text{Rs. }100$
$\displaystyle \text{Market price of one share}=100+10\%\text{ of }100=\text{Rs. }110$
$\displaystyle \text{Number of shares bought}=\frac{8800}{110}=80$
$\displaystyle \text{Let the dividend per cent be }x\%.$
$\displaystyle 80\times100\times\frac{x}{100}=1200$
$\displaystyle 80x=1200$
$\displaystyle x=15$
$\displaystyle \therefore \text{(i) Number of shares}=80,\quad \text{(ii) Dividend per cent}=15\%$
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$\displaystyle \textbf{Question 14: } \text{A man invests Rs. }1680\text{ in buying shares of nominal value}$
$\displaystyle \text{Rs. }24\text{ and selling at }12\%\text{ premium. The dividend on the shares is}$
$\displaystyle 15\%\text{ per annum. Calculate: (i) The number of shares he buys;}$
$\displaystyle \text{(ii) The dividend he receives. }\text{[ICSE 1999]}$
$\displaystyle \text{Answer:}$
$\displaystyle \text{Nominal value of one share}=\text{Rs. }24$
$\displaystyle \text{Market price of one share}=24+12\%\text{ of }24$
$\displaystyle =24+24\times\frac{12}{100}=\text{Rs. }26.88$
$\displaystyle \text{Number of shares bought}=\frac{1680}{26.88}=62.5$
$\displaystyle \text{Dividend received}=62.5\times24\times\frac{15}{100}=\text{Rs. }225$
$\displaystyle \therefore \text{(i) Number of shares}=62.5,\quad \text{(ii) Dividend received}=\text{Rs. }225$
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$\displaystyle \textbf{Question 15: } \text{By investing Rs. }7500\text{ in a company paying }10\%\text{ dividend,}$
$\displaystyle \text{an annual income of Rs. }500\text{ is received. What price is paid for each}$
$\displaystyle \text{Rs. }100\text{ share?}\hfill \text{[ICSE 1990]}$
$\displaystyle \text{Answer:}$
$\displaystyle \text{Let the premium on each share be Rs. }x.$
$\displaystyle \text{Then, the market price of one share}=(100+x)\text{ Rs.}$
$\displaystyle \text{Number of shares bought}=\frac{7500}{100+x}$
$\displaystyle \frac{7500}{100+x}\times100\times\frac{10}{100}=500$
$\displaystyle \frac{7500}{100+x}\times10=500$
$\displaystyle 75000=500(100+x)$
$\displaystyle 75000=50000+500x$
$\displaystyle 25000=500x$
$\displaystyle x=50$
$\displaystyle \therefore \text{Price paid for each share}=100+50=\text{Rs. }150$
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