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.

Answer:

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.

Answer:

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.

Answer:

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.

Answer:

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.

Answer:

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?

Answer:

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\% .

Answer:

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.

Answer:

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

Answer:

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.

Answer:

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]

Answer:

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;

Answer:

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.

Answer:

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.

Answer:

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;

Answer:

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]

Answer:

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]

Answer:

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]

Answer:

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]

Answer:

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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