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.

Nominal Value of the share $= 40 \ Rs.$

Market Value of the share $= 56 \ Rs.$

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

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

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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.

Nominal Value of the share $= 40 \ Rs.$

Market Value of the share $= 24 \ Rs.$

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

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

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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.

Nominal Value of the share $= 50 \ Rs.$

Market Value of the share $= 44 \ Rs.$

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

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

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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.

Nominal Value of the share $= 80 \ Rs.$

Market Value of the share $= 104 \ Rs.$

Market Value of 150 shares $= 150 \times 104 = 15600 \ Rs.$

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

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

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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.

Nominal Value of the share $= 10 \ Rs.$

Market Value of the share $= 12.50 \ Rs.$

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

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

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

Loss $= 270 \times (12.50-10) = 675 \ Rs.$

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

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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?

Nominal Value of the share $= 100 \ Rs.$

Market Value of the share $= 150 \ Rs.$

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

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

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

Hence the investment $= 40 \times 150 = 6000 \ Rs.$

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

Nominal Value of the share $= 60 \ Rs.$

Market Value of the share $= 50 \ Rs.$

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

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

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.

Nominal Value of the share $= 100 \ Rs.$

Market Value of the share $= 85 \ Rs.$

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

Hence Investment $= 150 \times 85 = 12750 \ Rs.$

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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

Nominal Value of the share $= 60 \ Rs.$

Market Value of the share $= x \ Rs.$

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

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

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

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

Hence the investment $= 200 \times 50 = 10000 \ Rs.$

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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

Nominal Value of the share $= 10 \ Rs.$

Market Value of the share $= 13 \ Rs.$

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

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

Second Investment

Nominal Value of the share $= 10 \ Rs.$

Market Value of the share $= 16 \ Rs.$

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

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

Therefore the first investment is better.

Let us say that he invests $x \ Rs.$ in both the investments

Therefore

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

$3.846x = 3.75 x = 30 \Rightarrow x = 31200 \ Rs.$

Hence total investment $= 31200+31200 = 62400 \ Rs.$

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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]

Nominal Value of the share $= 100 \ Rs.$

Market Value of the share $= 125 \ Rs.$

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

Selling Value of the share $= 140 \ Rs.$

Amount of money raised $= 8400 \ Rs.$

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

Shares left $= 360 - 60 = 300$

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

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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;

Nominal Value of the share $= 100 \ Rs.$

Market Value of the share $= 120 \ Rs.$

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

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

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

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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.

Nominal Value of the share $= 150 \ Rs.$

Market Value of the share $= x \ Rs.$

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

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

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

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

Hence the investment $= 75 \times 180 = 13500 \ Rs.$

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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 $= x \ Rs.$

Nominal Value of the share $= 100 \ Rs.$

Market Value of the share $= 92 \ Rs.$

Dividend earned $= 8\%$

Second Investment

Therefore  the amount invested $= (50760-x) \ Rs.$

Nominal Value of the share $= 100 \ Rs.$

Market Value of the share $= 108 \ Rs.$

Dividend earned $= 9\%$

Given that dividend earned in both investments is equal.

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

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

$864x = 828(50760-x)$

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

Hence the first investment $= 24840 \ Rs.$ and second investment $= 25920 \ Rs.$

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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 $= \frac{x}{3} \ Rs.$

Nominal Value of the share $= 50 \ Rs.$

Market Value of the share $= 60 \ Rs.$

Dividend earned $= 20\%$

Second Investment

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

Nominal Value of the share $= 100 \ Rs.$

Market Value of the share $= 110 \ Rs.$

Dividend earned $= 10\%$

Given that dividend earned in both investments is 9200 Rs.

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

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

$x = 79200$

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

Hence the first investment $= 24840 \ Rs.$ and second investment $= 25920 \ Rs.$

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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 dividend.     [2010]

First Investment

Let the amount invested $= 4500 \ Rs.$

Nominal Value of the share $= 10 \ Rs.$

Market Value of the share $= 15 \ Rs.$

Dividend earned $= 8\%$

Number of shares bought $= \frac{4500}{15} = 300$

Sale Proceed $= 300 \times 30 = 9000 \ Rs.$

Dividend earned $= 300 \times 10 \times \frac{8}{100} = 240 \ Rs.$

Second Investment

Therefore  the amount invested $= 9000 \ Rs.$

Nominal Value of the share $= 100 \ Rs.$

Market Value of the share $= 125 \ Rs.$

Dividend earned $= 12\%$

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

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

Hence the change in income $= 720-240 = 480 \ Rs.$

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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]

Nominal Value of the share $= 100 \ Rs.$

Market Value of the share $= 80 \ Rs.$

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

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

Sale proceeds $= 650 \times 120 = 78000 \ Rs.$

Profit $= (78000-52000)+5200 = 31200 \ Rs.$

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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]

Nominal Value of the share $= 100 \ Rs.$

Market Value of the share $= 132 \ Rs.$

Number of shares bought $= 50$

Investment $= 50 \times 132 = 6600 \ Rs.$

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

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

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

Nominal Value of the share $= 50 \ Rs.$

Market Value of the share $= 60 \ Rs.$

Dividend earned $= 15\%$

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

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

Investment $= 80 \times 60 = 4800 \ Rs.$

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

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