Question 1: A man bought Rs. 40 shares at a premium of 40%. Find his income, if he invests Rs. 14,000 in these shares and receives a dividend at the rate of 8% on the face value of the shares.

$\displaystyle \text{Nominal Value of the share } = 40 \text{ Rs. }$

$\displaystyle \text{Market Value of the share } = 56 \text{ Rs. }$

$\displaystyle \text{Number of shares bought } = \frac{14000}{56} = 250$

$\displaystyle \text{Dividend earned } = 250 \times 40 \times \frac{8}{100} = 800 \text{ Rs. }$

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Question 2: A man bought Rs. 40 shares at a discount of 40%. Find his income, if he invests Rs. 12,000 in these shares and receives a dividend at the rate of 11% on the face value of the shares.

$\displaystyle \text{Nominal Value of the share } = 40 \text{ Rs. }$

$\displaystyle \text{Market Value of the share } = 24 \text{ Rs. }$

$\displaystyle \text{Number of shares bought } = \frac{12000}{24} = 500$

$\displaystyle \text{Dividend earned } = 500 \times 40 \times \frac{11}{100} = 2200 \text{ Rs. }$

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Question 3: A sum of Rs. 11,800 is invested in Rs. 50 shares available at 12% discount. Find the income, if a dividend of 12% is given on the shares.

$\displaystyle \text{Nominal Value of the share } = 50 \text{ Rs. }$

$\displaystyle \text{Market Value of the share } = 44 \text{ Rs. }$

$\displaystyle \text{Number of shares bought } = \frac{11880}{44} = 270$

$\displaystyle \text{Dividend earned } = 270 \times 50 \times \frac{12}{100} = 1620 \text{ Rs. }$

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Question 4: A man buys buys Rs. 80 shares at 30% premium in a company paying 18% dividend. Find: i) The market value of 150 shares; ii) His annual income from these shares. iii) His % return from this investment.

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

$\displaystyle \text{Market Value of the share } = 104 \text{ Rs. }$

Market Value of 150 shares $\displaystyle = 150 \times 104 = 15600 \text{ Rs. }$

$\displaystyle \text{Dividend earned } = 150 \times 80 \times \frac{18}{100} = 2160 \text{ Rs. }$

$\displaystyle \% \text{ return: } = \frac{2160}{15600} \times 100 = 13.85\%$

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Question 5: A person invests Rs. 5625 in a company paying 7% per annum when a share of Rs. 10 stands for Rs. 12.50. Find his income from this investment. If he sells 60% of these shares for Rs. 10 each. Find his gain or loss in this transaction.

$\displaystyle \text{Nominal Value of the share } = 10 \text{ Rs. }$

$\displaystyle \text{Market Value of the share } = 12.50 \text{ Rs. }$

$\displaystyle \text{Number of shares bought } = \frac{5625}{12.50} = 450$

$\displaystyle \text{Dividend earned } = 450 \times 10 \times \frac{7}{100} = 315 \text{ Rs. }$

$\displaystyle \text{Number of shares sold } = \frac{60}{100} \times 470 = 270$

$\displaystyle \text{Loss } = 270 \times (12.50-10) = 675 \text{ Rs. }$

$\displaystyle \% \text{ return: } (loss) = \frac{675}{270 \times 12.5} \times 100 = 20\%$

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Question 6: A person buys 85 shares (par value Rs. 100) at Rs. 150 each. i) If the dividend is 6.5%, what will be her annual income? ii) In order to increase her income by Rs. 260; how much more should she invest?

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

$\displaystyle \text{Market Value of the share } = 150 \text{ Rs. }$

$\displaystyle \text{Dividend earned } = 85 \times 100 \times \frac{6.5}{100} = 552.50 \text{ Rs. }$

$\displaystyle \text{Dividend earned on one share } = 1 \times 100 \times \frac{6.5}{100} = 6.50 \text{ Rs. }$

$\displaystyle \text{Therefore to earn 260 Rs. more the person needs to buy } = \frac{260}{6.5} = 40 \text{ more shares. }$

Hence the investment $\displaystyle = 40 \times 150 = 6000 \text{ Rs. }$

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Question 7: A company gives $\displaystyle x\%$ dividend on its Rs. 60 shares, whereas the return on the investment in these shares is $\displaystyle (x+3)\%$latex \displaystyle . If the market value of each share is Rs. 50, find the value of $\displaystyle x\%$ .

$\displaystyle \text{Nominal Value of the share } = 60 \text{ Rs. }$

$\displaystyle \text{Market Value of the share } = 50 \text{ Rs. }$

$\displaystyle \text{Dividend earned } = 100 \times 60 \times \frac{x}{100} = 60x \text{ Rs. }$

$\displaystyle \% \text{ return: } = \frac{60x}{100 \times 50} \times 100 = \frac{6}{5} x\%$

$\displaystyle \text{Hence } \frac{6}{5} x = x+3 \Rightarrow x = 15\%$

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Question 8: How much should a man invest in Rs. 100 shares selling at Rs.85 to obtain an annual income of Rs. 1,800; If the dividend declared is 12%? Also, find the percentage return on this investment.

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

$\displaystyle \text{Market Value of the share } = 85 \text{ Rs. }$

$\displaystyle \text{Dividend earned } 1800 = x \times 100 \times \frac{12}{100} \Rightarrow x=150 \text{ Rs. }$

Hence Investment $\displaystyle = 150 \times 85 = 12750 \text{ Rs. }$

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Question 9: A dividend of 10% was declared on shares with a face value of Rs. 60. If the rate of return is 12%, calculate: i) The market value of the share. ii) The amount to be invested to get an annual income of Rs. 1,200

$\displaystyle \text{Nominal Value of the share } = 60 \text{ Rs. }$

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

$\displaystyle \text{Dividend earned } = 100 \times 60 \times \frac{10}{100} = 600 \text{ Rs. }$

$\displaystyle \% \text{ return: } \frac{600}{100 \times x} \times 100 = \frac{12}{100} \Rightarrow x = 50 \text{ Rs. }$

$\displaystyle \text{Dividend earned on one share } = 1 \times 60 \times \frac{10}{100} = 6 \text{ Rs. }$

$\displaystyle \text{Therefore to earn 1200 Rs. more the person needs to buy } = \frac{1200}{6} = 200 \text{more shares. }$

Hence the investment $\displaystyle = 200 \times 50 = 10000 \text{ Rs. }$

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Question 10: A person has a choice to invest in ten-rupees shares of two firms at Rs. 13 or at Rs. 16. If the first firm pays 5% dividend and the second firm pays 6%dividend per annum, find: i) Which firm is paying better; ii) If he invests equally in both the firms and the difference between the returns from them is Rs. 30, find how much, in all, does he invest.

First Investment

$\displaystyle \text{Nominal Value of the share } = 10 \text{ Rs. }$

$\displaystyle \text{Market Value of the share } = 13 \text{ Rs. }$

$\displaystyle \text{Dividend earned } = 100 \times 10 \times \frac{5}{100} = 50 \text{ Rs. }$

$\displaystyle \% \text{ return: } \frac{50}{100 \times 13} \times 100 = 3.84\%$

Second Investment

$\displaystyle \text{Nominal Value of the share } = 10 \text{ Rs. }$

$\displaystyle \text{Market Value of the share } = 16 \text{ Rs. }$

$\displaystyle \text{Dividend earned } = 100 \times 10 \times \frac{6}{100} = 60 \text{ Rs. }$

$\displaystyle \% \text{ return: } \frac{60}{100 \times 16} \times 100 = 3.75\%$

Therefore the first investment is better.

Let us say that he invests $\displaystyle x \text{ Rs. }$ in both the investments

Therefore

$\displaystyle \frac{x}{13} \times 10 \times \frac{5}{100} - \frac{x}{16} \times 10 \times \frac{6}{100} = 30$

$\displaystyle 3.846x = 3.75 x = 30 \Rightarrow x = 31200 \text{ Rs. }$

Hence total investment $\displaystyle = 31200+31200 = 62400 \text{ Rs. }$

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Question 11: 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. [2004]

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

$\displaystyle \text{Market Value of the share } = 125 \text{ Rs. }$

$\displaystyle \text{Number of shares bought } = \frac{45000}{125} = 360$

Selling Value of the share $\displaystyle = 140 \text{ Rs. }$

Amount of money raised $\displaystyle = 8400 \text{ Rs. }$

$\displaystyle \text{Therefore number of shares sold }= \frac{8400}{140} = 60$

Shares left $\displaystyle = 360 - 60 = 300$

$\displaystyle \text{Dividend earned on remaining shares }= 300 \times 100 \times \frac{15}{100} = 4500 \text{ Rs. }$

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Question 12: A person invested Rs. 29,040 in 15% Rs.100 shares quoted at a premium of 20%. Calculate; i) The number of shares bought by him; ii) His income from the investment. ii) The percentage return on his investment;

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

$\displaystyle \text{Market Value of the share } = 120 \text{ Rs. }$

$\displaystyle \text{Number of shares bought } = \frac{29040}{120} = 242$

$\displaystyle \text{Dividend earned } = 242 \times 100 \times \frac{15}{100} = 3630 \text{ Rs. }$

$\displaystyle \% \text{ return: } = \frac{3630}{242 \times 120} \times 100 = 12.5\%$

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Question 13: A dividend of 12% was declared on Rs. 150 shares selling at a certain price. If the rate of return is 10%, calculate: i) The market value of the shares. ii) The amount to be invested to obtain an annual dividend of Rs. 1,350.

$\displaystyle \text{Nominal Value of the share } = 150 \text{ Rs. }$

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

$\displaystyle \text{Dividend earned } = 100 \times 150 \times \frac{12}{100} = 1800 \text{ Rs. }$

$\displaystyle \% \text{ return: } \Rightarrow \frac{1800}{100 \times x} \times 100 = \frac{10}{100} \Rightarrow x = 180 \text{ Rs. }$

$\displaystyle \text{Dividend earned on one share } = 1 \times 150 \times \frac{12}{100} = 18 \text{ Rs. }$

$\displaystyle \text{Therefore to earn 1350 Rs. more the person needs to buy } = \frac{1350}{18} = 75 \text{ more shares. }$

Hence the investment $\displaystyle = 75 \times 180 = 13500 \text{ Rs. }$

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Question 14: Divide Rs. 50,760 into two parts such that if one part is invested in 8% Rs. 100 shares at 8% discount and the other in 9% Rs. 100 shares at 8% premium, the annual incomes from both the investments are equal.

First Investment

Let the amount invested $\displaystyle = x \text{ Rs. }$

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

$\displaystyle \text{Market Value of the share } = 92 \text{ Rs. }$

$\displaystyle \text{Dividend earned } = 8\%$

Second Investment

Therefore the amount invested $\displaystyle = (50760-x) \text{ Rs. }$

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

$\displaystyle \text{Market Value of the share } = 108 \text{ Rs. }$

$\displaystyle \text{Dividend earned } = 9\%$

Given that dividend earned in both investments is equal.

$\displaystyle \frac{x}{92} \times 100 \times \frac{8}{100} = \frac{50760-x}{108} \times 100 \times \frac{9}{100}$

$\displaystyle \frac{8x}{92} = 9( \frac{50760-x}{108})$

$\displaystyle 864x = 828(50760-x)$

$\displaystyle \Rightarrow x = \frac{828 \times 50760}{1692} = 24840 \text{ Rs. }$

Hence the first investment $\displaystyle = 24840 \text{ Rs. }$ and second investment $\displaystyle = 25920 \text{ Rs. }$

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Question 15: A person invested of his saving in 20% Rs. 50 shares quoted at Rs. 60 and the remainder of the savings in 10% Rs. 100 shares quoted at Rs. 110. if his total income from these investments is Rs. 9,200; find: i) His total savings ii) The number of Rs. 50 shares; ii) The number of Rs. 100 shares;

First Investment

Let the amount invested $\displaystyle = \frac{x}{3} \text{ Rs. }$

$\displaystyle \text{Nominal Value of the share } = 50 \text{ Rs. }$

$\displaystyle \text{Market Value of the share } = 60 \text{ Rs. }$

$\displaystyle \text{Dividend earned } = 20\%$

Second Investment

Therefore the amount invested $\displaystyle = \frac{2}{3} x \text{ Rs. }$

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

$\displaystyle \text{Market Value of the share } = 110 \text{ Rs. }$

$\displaystyle \text{Dividend earned } = 10\%$

Given that dividend earned in both investments is 9200 Rs.

$\displaystyle \frac{\frac{x}{3}}{60} \times 50 \times \frac{20}{100} + \frac{\frac{2x}{3}}{110} \times 100 \times \frac{10}{100} = 9200$

$\displaystyle \frac{x}{18} + \frac{2x}{33} = 9200$

$\displaystyle x = 79200$

$\displaystyle \Rightarrow x = \frac{828 \times 50760}{1692} = 24840 \text{ Rs. }$

Hence the first investment $\displaystyle = 24840 \text{ Rs. }$ and second investment $\displaystyle = 25920 \text{ Rs. }$

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Question 16: 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 the dividend. [2010]

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 $\displaystyle = 9000 \text{ Rs. }$

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

$\displaystyle \text{Market Value of the share } = 125 \text{ Rs. }$

$\displaystyle \text{Dividend earned } = 12\%$

$\displaystyle \text{Number of shares bought } = \frac{9000}{125} = 72$

$\displaystyle \text{Dividend earned } = 72 \times 100 \times \frac{12}{100} = 720 \text{ Rs. }$

Hence the change in income $\displaystyle = 720-240 = 480 \text{ Rs. }$

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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]

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

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

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

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

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

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

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Question 18: 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? [2013]

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

$\displaystyle \text{Market Value of the share } = 132 \text{ Rs. }$

$\displaystyle \text{Number of shares bought } = 50$

Investment $\displaystyle = 50 \times 132 = 6600 \text{ Rs. }$

$\displaystyle \text{Dividend earned } = 50 \times 100 \times \frac{7.5}{100} = 375 \text{ Rs. }$

$\displaystyle \text{Dividend earned on one share } = 1 \times 100 \times \frac{7.5}{100} = 7.5 \text{ Rs. }$

$\displaystyle \text{Therefore to earn 150 Rs. more, one needs to buy } \frac{150}{7.5} = 20 \text{ shares. }$

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Question 19: 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. [2004]

$\displaystyle \text{Nominal Value of the share } = 50 \text{ Rs. }$

$\displaystyle \text{Market Value of the share } = 60 \text{ Rs. }$

$\displaystyle \text{Dividend earned } = 15\%$

$\displaystyle \text{Dividend earned on one share } = 1 \times 50 \times \frac{15}{100} = 7.5 \text{ Rs. }$

$\displaystyle \text{Number of shares bought } = \frac{600}{7.5} = 80$

Investment $\displaystyle = 80 \times 60 = 4800 \text{ Rs. }$

$\displaystyle \% \text{ return: } = \frac{600}{4800} \times 100 = 12.5\%$