Class 10: Shares and Dividend

$\displaystyle \textbf{Question 1: } \text{A man bought Rs. }40\text{ shares at a premium of }40\%.$
$\displaystyle \text{Find his income, if he invests Rs. }14000\text{ in these shares and receives}$
$\displaystyle \text{a dividend at the rate of }8\%\text{ on the face value of the shares.}$
$\displaystyle \text{Answer:}$
$\displaystyle \text{Nominal value of one share}=\text{Rs. }40$
$\displaystyle \text{Market price of one share}=40+40\%\text{ of }40=\text{Rs. }56$
$\displaystyle \text{Number of shares bought}=\frac{14000}{56}=250$
$\displaystyle \text{Annual income}=250\times40\times\frac{8}{100}=\text{Rs. }800$
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$\displaystyle \textbf{Question 2: } \text{A man bought Rs. }40\text{ shares at a discount of }40\%.$
$\displaystyle \text{Find his income, if he invests Rs. }12000\text{ in these shares and receives}$
$\displaystyle \text{a dividend at the rate of }11\%\text{ on the face value of the shares.}$
$\displaystyle \text{Answer:}$
$\displaystyle \text{Nominal value of one share}=\text{Rs. }40$
$\displaystyle \text{Market price of one share}=40-40\%\text{ of }40=\text{Rs. }24$
$\displaystyle \text{Number of shares bought}=\frac{12000}{24}=500$
$\displaystyle \text{Annual income}=500\times40\times\frac{11}{100}=\text{Rs. }2200$
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$\displaystyle \textbf{Question 3: } \text{A sum of Rs. }11880\text{ is invested in Rs. }50\text{ shares}$
$\displaystyle \text{available at }12\%\text{ discount. Find the income, if a dividend of }12\%$
$\displaystyle \text{is given on the shares.}$
$\displaystyle \text{Answer:}$
$\displaystyle \text{Nominal value of one share}=\text{Rs. }50$
$\displaystyle \text{Market price of one share}=50-12\%\text{ of }50=\text{Rs. }44$
$\displaystyle \text{Number of shares bought}=\frac{11880}{44}=270$
$\displaystyle \text{Annual income}=270\times50\times\frac{12}{100}=\text{Rs. }1620$
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$\displaystyle \textbf{Question 4: } \text{A man buys Rs. }80\text{ shares at }30\%\text{ premium in a company}$
$\displaystyle \text{paying }18\%\text{ dividend. Find: (i) The market value of }150\text{ shares}$
$\displaystyle \text{(ii) His annual income from these shares (iii) His percentage return}$
$\displaystyle \text{from this investment.}$
$\displaystyle \text{Answer:}$
$\displaystyle \text{Nominal value of one share}=\text{Rs. }80$
$\displaystyle \text{Market price of one share}=80+30\%\text{ of }80=\text{Rs. }104$
$\displaystyle \text{Market value of }150\text{ shares}=150\times104=\text{Rs. }15600$
$\displaystyle \text{Annual income}=150\times80\times\frac{18}{100}=\text{Rs. }2160$
$\displaystyle \text{Percentage return}=\frac{2160}{15600}\times100=13.85\%$
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$\displaystyle \textbf{Question 5: } \text{A person invests Rs. }5625\text{ in a company paying }7\%\text{ per annum}$
$\displaystyle \text{when a Rs. }10\text{ share stands at Rs. }12.50.\text{ Find his income from this}$
$\displaystyle \text{investment. If he sells }60\%\text{ of these shares for Rs. }10\text{ each, find}$
$\displaystyle \text{his gain or loss in this transaction.}$
$\displaystyle \text{Answer:}$
$\displaystyle \text{Nominal value of one share}=\text{Rs. }10$
$\displaystyle \text{Market price of one share}=\text{Rs. }12.50$
$\displaystyle \text{Number of shares bought}=\frac{5625}{12.50}=450$
$\displaystyle \text{Annual income}=450\times10\times\frac{7}{100}=\text{Rs. }315$
$\displaystyle \text{Number of shares sold}=\frac{60}{100}\times450=270$
$\displaystyle \text{Loss}=270\times(12.50-10)=270\times2.50=\text{Rs. }675$
$\displaystyle \therefore \text{He incurs a loss of Rs. }675.$
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$\displaystyle \textbf{Question 6: } \text{A person buys }85\text{ shares (par value Rs. }100\text{) at}$
$\displaystyle \text{Rs. }150\text{ each. (i) If the dividend is }6.5\%,\text{ what will be her annual}$
$\displaystyle \text{income? (ii) In order to increase her income by Rs. }260,\text{ how much more}$
$\displaystyle \text{should she invest?}$
$\displaystyle \text{Answer:}$
$\displaystyle \text{Nominal value of one share}=\text{Rs. }100$
$\displaystyle \text{Market price of one share}=\text{Rs. }150$
$\displaystyle \text{Annual income}=85\times100\times\frac{6.5}{100}=\text{Rs. }552.50$
$\displaystyle \text{Dividend per share}=100\times\frac{6.5}{100}=\text{Rs. }6.50$
$\displaystyle \text{Additional shares required}=\frac{260}{6.50}=40$
$\displaystyle \therefore \text{Additional investment}=40\times150=\text{Rs. }6000$
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$\displaystyle \textbf{Question 7: } \text{A company gives }x\%\text{ dividend on its Rs. }60\text{ shares,}$
$\displaystyle \text{whereas the return on the investment in these shares is }(x+3)\%.$
$\displaystyle \text{If the market value of each share is Rs. }50,\text{ find the value of }x.$
$\displaystyle \text{Answer:}$
$\displaystyle \text{Nominal value of one share}=\text{Rs. }60$
$\displaystyle \text{Market price of one share}=\text{Rs. }50$
$\displaystyle \text{Dividend on }100\text{ shares}=100\times60\times\frac{x}{100}=60x\text{ Rs.}$
$\displaystyle \text{Percentage return}=\frac{60x}{100\times50}\times100=\frac{6x}{5}\%$
$\displaystyle \frac{6x}{5}=x+3$
$\displaystyle 6x=5x+15$
$\displaystyle x=15$
$\displaystyle \therefore \text{Dividend rate}=15\%$
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$\displaystyle \textbf{Question 8: } \text{How much should a man invest in Rs. }100\text{ shares selling at}$
$\displaystyle \text{Rs. }85\text{ to obtain an annual income of Rs. }1800,\text{ if the dividend}$
$\displaystyle \text{declared is }12\%\text{? Also, find the percentage return on this investment.}$
$\displaystyle \text{Answer:}$
$\displaystyle \text{Nominal value of one share}=\text{Rs. }100$
$\displaystyle \text{Market price of one share}=\text{Rs. }85$
$\displaystyle \text{Let the number of shares bought}=x$
$\displaystyle x\times100\times\frac{12}{100}=1800$
$\displaystyle 12x=1800$
$\displaystyle x=150$
$\displaystyle \text{Amount invested}=150\times85=\text{Rs. }12750$
$\displaystyle \text{Percentage return}=\frac{1800}{12750}\times100=14.12\%$
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$\displaystyle \textbf{Question 9: } \text{A dividend of }10\%\text{ was declared on shares with face value Rs. }60.$
$\displaystyle \text{If the rate of return is }12\%,\text{ calculate: (i) The market value of the share}$
$\displaystyle \text{(ii) The amount to be invested to get an annual income of Rs. }1200.$
$\displaystyle \text{Answer:}$
$\displaystyle \text{Nominal value of one share}=\text{Rs. }60$
$\displaystyle \text{Let the market price of one share}=\text{Rs. }x$
$\displaystyle \text{Dividend on one share}=60\times\frac{10}{100}=\text{Rs. }6$
$\displaystyle \frac{6}{x}\times100=12$
$\displaystyle 12x=600$
$\displaystyle x=50$
$\displaystyle \therefore \text{Market value of one share}=\text{Rs. }50$
$\displaystyle \text{Number of shares required}=\frac{1200}{6}=200$
$\displaystyle \therefore \text{Amount to be invested}=200\times50=\text{Rs. }10000$
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$\displaystyle \textbf{Question 10: } \text{A person has a choice to invest in Rs. }10\text{ shares of two firms}$
$\displaystyle \text{at Rs. }13\text{ or at Rs. }16.\text{ If the first firm pays }5\%\text{ dividend and the}$
$\displaystyle \text{second firm pays }6\%\text{ dividend per annum, find: (i) Which firm is better}$
$\displaystyle \text{(ii) If he invests equally in both firms and the difference between the returns}$
$\displaystyle \text{is Rs. }30,\text{ find how much, in all, does he invest.}$
$\displaystyle \text{Answer:}$
$\displaystyle \text{First firm:}$
$\displaystyle \text{Dividend on }100\text{ shares}=100\times10\times\frac{5}{100}=\text{Rs. }50$
$\displaystyle \text{Investment in }100\text{ shares}=100\times13=\text{Rs. }1300$
$\displaystyle \text{Return}\%=\frac{50}{1300}\times100=3.85\%$
$\displaystyle \text{Second firm:}$
$\displaystyle \text{Dividend on }100\text{ shares}=100\times10\times\frac{6}{100}=\text{Rs. }60$
$\displaystyle \text{Investment in }100\text{ shares}=100\times16=\text{Rs. }1600$
$\displaystyle \text{Return}\%=\frac{60}{1600}\times100=3.75\%$
$\displaystyle \therefore \text{The first firm gives a better return.}$
$\displaystyle \text{Let the amount invested in each firm be Rs. }x.$
$\displaystyle \frac{x}{13}\times10\times\frac{5}{100}-\frac{x}{16}\times10\times\frac{6}{100}=30$
$\displaystyle \frac{x}{26}-\frac{3x}{80}=30$
$\displaystyle \frac{40x-39x}{1040}=30$
$\displaystyle x=31200$
$\displaystyle \therefore \text{Total investment}=31200+31200=\text{Rs. }62400$
$\\$

$\displaystyle \textbf{Question 11: } \text{A man invested Rs. }45000\text{ in }15\%\text{ Rs. }100\text{ shares quoted}$
$\displaystyle \text{at Rs. }125.\text{ When the market value of these shares rose to Rs. }140,\text{ he sold}$
$\displaystyle \text{some shares, just enough to raise Rs. }8400.\text{ Calculate: (i) The number of}$
$\displaystyle \text{shares he still holds \quad (ii) The dividend due to him on these remaining shares.}$
$\displaystyle \hfill \text{[ICSE 2004]}$
$\displaystyle \text{Answer:}$
$\displaystyle \text{Nominal value of one share}=\text{Rs. }100$
$\displaystyle \text{Market price of one share}=\text{Rs. }125$
$\displaystyle \text{Number of shares bought}=\frac{45000}{125}=360$
$\displaystyle \text{Selling price of one share}=\text{Rs. }140$
$\displaystyle \text{Number of shares sold}=\frac{8400}{140}=60$
$\displaystyle \text{Number of shares remaining}=360-60=300$
$\displaystyle \text{Dividend on remaining shares}=300\times100\times\frac{15}{100}=\text{Rs. }4500$
$\\$

$\displaystyle \textbf{Question 12: } \text{A person invested Rs. }29040\text{ in }15\%\text{ Rs. }100\text{ shares}$
$\displaystyle \text{quoted at a premium of }20\%.\text{ Calculate: (i) The number of shares bought}$
$\displaystyle \text{(ii) His income from the investment \quad (iii) The percentage return on his}$
$\displaystyle \text{investment.}$
$\displaystyle \text{Answer:}$
$\displaystyle \text{Nominal value of one share}=\text{Rs. }100$
$\displaystyle \text{Market price of one share}=100+20\%\text{ of }100=\text{Rs. }120$
$\displaystyle \text{Number of shares bought}=\frac{29040}{120}=242$
$\displaystyle \text{Annual income}=242\times100\times\frac{15}{100}=\text{Rs. }3630$
$\displaystyle \text{Percentage return}=\frac{3630}{29040}\times100=12.5\%$
$\\$

$\displaystyle \textbf{Question 13: } \text{A dividend of }12\%\text{ was declared on Rs. }150\text{ shares selling}$
$\displaystyle \text{at a certain price. If the rate of return is }10\%,\text{ calculate:}$
$\displaystyle \text{(i) The market value of the shares \quad (ii) The amount to be invested}$
$\displaystyle \text{to obtain an annual dividend of Rs. }1350.$
$\displaystyle \text{Answer:}$
$\displaystyle \text{Nominal value of one share}=\text{Rs. }150$
$\displaystyle \text{Let the market price of one share}=\text{Rs. }x$
$\displaystyle \text{Dividend on one share}=150\times\frac{12}{100}=\text{Rs. }18$
$\displaystyle \frac{18}{x}\times100=10$
$\displaystyle 10x=1800$
$\displaystyle x=180$
$\displaystyle \therefore \text{Market value of one share}=\text{Rs. }180$
$\displaystyle \text{Number of shares required}=\frac{1350}{18}=75$
$\displaystyle \therefore \text{Amount to be invested}=75\times180=\text{Rs. }13500$
$\\$

$\displaystyle \textbf{Question 14: } \text{Divide Rs. }50760\text{ into two parts such that if one part}$
$\displaystyle \text{is invested in }8\%\text{ Rs. }100\text{ shares at }8\%\text{ discount and the other}$
$\displaystyle \text{in }9\%\text{ Rs. }100\text{ shares at }8\%\text{ premium, the annual incomes}$
$\displaystyle \text{from both the investments are equal.}$
$\displaystyle \text{Answer:}$
$\displaystyle \text{Let the amount invested in first shares}=\text{Rs. }x$
$\displaystyle \text{Then, amount invested in second shares}=(50760-x)\text{ Rs.}$
$\displaystyle \text{Market price of one first share}=100-8\%\text{ of }100=\text{Rs. }92$
$\displaystyle \text{Market price of one second share}=100+8\%\text{ of }100=\text{Rs. }108$
$\displaystyle \text{Since the annual incomes from both investments are equal,}$
$\displaystyle \frac{x}{92}\times100\times\frac{8}{100}=\frac{50760-x}{108}\times100\times\frac{9}{100}$
$\displaystyle \frac{8x}{92}=\frac{9(50760-x)}{108}$
$\displaystyle 864x=828(50760-x)$
$\displaystyle 864x=42029280-828x$
$\displaystyle 1692x=42029280$
$\displaystyle x=24840$
$\displaystyle \therefore \text{First part}=\text{Rs. }24840$
$\displaystyle \text{Second part}=50760-24840=\text{Rs. }25920$
$\\$

$\displaystyle \textbf{Question 15: } \text{A person invested one-third of his savings in }20\%\text{ Rs. }50\text{ shares}$
$\displaystyle \text{quoted at Rs. }60\text{ and the remainder of the savings in }10\%\text{ Rs. }100\text{ shares}$
$\displaystyle \text{quoted at Rs. }110.\text{ If his total income from these investments is Rs. }9200,$
$\displaystyle \text{find: (i) His total savings \quad (ii) The number of Rs. }50\text{ shares}$
$\displaystyle \text{(iii) The number of Rs. }100\text{ shares.}$
$\displaystyle \text{Answer:}$
$\displaystyle \text{Let his total savings be Rs. }x.$
$\displaystyle \text{Amount invested in }20\%\text{ Rs. }50\text{ shares}=\frac{x}{3}$
$\displaystyle \text{Amount invested in }10\%\text{ Rs. }100\text{ shares}=\frac{2x}{3}$
$\displaystyle \frac{\frac{x}{3}}{60}\times50\times\frac{20}{100}+\frac{\frac{2x}{3}}{110}\times100\times\frac{10}{100}=9200$
$\displaystyle \frac{x}{18}+\frac{2x}{33}=9200$
$\displaystyle \frac{11x+12x}{198}=9200$
$\displaystyle \frac{23x}{198}=9200$
$\displaystyle x=\frac{9200\times198}{23}=\text{Rs. }79200$
$\displaystyle \text{Number of Rs. }50\text{ shares}=\frac{79200/3}{60}=\frac{26400}{60}=440$
$\displaystyle \text{Number of Rs. }100\text{ shares}=\frac{2\times79200/3}{110}=\frac{52800}{110}=480$
$\displaystyle \therefore \text{Total savings}=\text{Rs. }79200,\ \text{Rs. }50\text{ shares}=440,\ \text{Rs. }100\text{ shares}=480$
$\\$

$\displaystyle \textbf{Question 16: } \text{Vivek invests Rs. }4500\text{ in }8\%\text{ Rs. }10\text{ shares at Rs. }15.$
$\displaystyle \text{He sells the shares when the price rises to Rs. }30\text{ and invests the proceeds}$
$\displaystyle \text{in }12\%\text{ Rs. }100\text{ shares at Rs. }125.\text{ Calculate: (i) The sale proceeds}$
$\displaystyle \text{(ii) The number of Rs. }100\text{ shares he buys \quad (iii) The change in his annual}$
$\displaystyle \text{income from the dividend. }\text{[ICSE 2010]}$
$\displaystyle \text{Answer:}$
$\displaystyle \text{First investment:}$
$\displaystyle \text{Number of shares bought}=\frac{4500}{15}=300$
$\displaystyle \text{Sale proceeds}=300\times30=\text{Rs. }9000$
$\displaystyle \text{Annual dividend from first investment}=300\times10\times\frac{8}{100}=\text{Rs. }240$
$\displaystyle \text{Second investment:}$
$\displaystyle \text{Number of Rs. }100\text{ shares bought}=\frac{9000}{125}=72$
$\displaystyle \text{Annual dividend from second investment}=72\times100\times\frac{12}{100}=\text{Rs. }864$
$\displaystyle \text{Change in annual income}=864-240=\text{Rs. }624$
$\\$

Question 17: 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. [2011]

Answer:

$\displaystyle \text{Nominal Value of the share } = 100 \text{ Rs. }$

$\displaystyle \text{Market Value of the share } = 80 \text{ Rs. }$

$\displaystyle \text{Number of shares bought } = \frac{52000}{80} = 650$

$\displaystyle \text{Dividend earned } = 650 \times 100 \times \frac{8}{100} = 5200 \text{ Rs. }$

Sale proceeds $\displaystyle = 650 \times 120 = 78000 \text{ Rs. }$

Profit $\displaystyle = (78000-52000)+5200 = 31200 \text{ Rs. }$

$\displaystyle \\$

$\displaystyle \textbf{Question 18: } \text{Salman buys }50\text{ shares of face value Rs. }100\text{ available at}$
$\displaystyle \text{Rs. }132.\text{ (i) What is his investment? (ii) If the dividend is }7.5\%,$
$\displaystyle \text{what will be his annual income? (iii) If he wants to increase his annual}$
$\displaystyle \text{income by Rs. }150,\text{ how many extra shares should he buy? }\hfill \text{[ICSE 2013]}$
$\displaystyle \text{Answer:}$
$\displaystyle \text{Nominal value of one share}=\text{Rs. }100$
$\displaystyle \text{Market price of one share}=\text{Rs. }132$
$\displaystyle \text{Number of shares bought}=50$
$\displaystyle \text{Investment}=50\times132=\text{Rs. }6600$
$\displaystyle \text{Annual income}=50\times100\times\frac{7.5}{100}=\text{Rs. }375$
$\displaystyle \text{Dividend on one share}=100\times\frac{7.5}{100}=\text{Rs. }7.50$
$\displaystyle \text{Additional shares required}=\frac{150}{7.50}=20$
$\displaystyle \therefore \text{He should buy }20\text{ more shares.}$
$\\$

$\displaystyle \textbf{Question 19: } \text{Salman invests a sum of money in Rs. }50\text{ shares paying}$
$\displaystyle 15\%\text{ dividend quoted at }20\%\text{ premium. If his annual dividend is}$
$\displaystyle \text{Rs. }600,\text{ calculate: (i) The number of shares he bought}$
$\displaystyle \text{(ii) His total investment \quad (iii) The rate of return on his investment.}$
$\displaystyle \hfill \text{[ICSE 2004]}$
$\displaystyle \text{Answer:}$
$\displaystyle \text{Nominal value of one share}=\text{Rs. }50$
$\displaystyle \text{Market price of one share}=50+20\%\text{ of }50=\text{Rs. }60$
$\displaystyle \text{Dividend on one share}=50\times\frac{15}{100}=\text{Rs. }7.50$
$\displaystyle \text{Number of shares bought}=\frac{600}{7.50}=80$
$\displaystyle \text{Total investment}=80\times60=\text{Rs. }4800$
$\displaystyle \text{Rate of return}=\frac{600}{4800}\times100=12.5\%$
$\\$