Class 10: Shares and Dividend – Exercise 5(a) – ICSE / ISC / CBSE Mathematics Portal for K12 Students

Question 1: How much money will be required to buy 200, Rs. 25 shares at a premium of Rs. 2?

Answer:

Market price of the share $\displaystyle = 25+2 = 27 \text{ Rs. }$

Therefore the money required to buy $\displaystyle 200$ shares $\displaystyle = 200 \times 27 = 5400 \text{ Rs. }$

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Question 2: How much money will be required to buy 125, Rs. 30 shares at a discount of Rs. 3?

Answer:

Market price of the share $\displaystyle = 30-3 = 27 \text{ Rs. }$

Therefore the money required to buy $\displaystyle 125$ shares $\displaystyle = 125 \times 27 = 3429 \text{ Rs. }$

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Question 3: A person buys 120 shares at a nominal value of Rs. 40 each, which he sells at Rs. 42.50 each. Find his profit and profit per cent.

Answer:

Profit per share $\displaystyle = 42.50-40 = 2.5 \text{ Rs. }$

Total investment $\displaystyle = 120 \times 40= 4800 \text{ Rs. }$

Total profit $\displaystyle = 120 \times 2.5= 300 \text{ Rs. }$

$\displaystyle \text{Profit} \% = \frac{300}{4800} \times 100 = 6\%$

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Question 4: Find the cost of 85 shares of Rs. 60 each when quoted at Rs. 63.25.

Answer:

Total cost of $\displaystyle 85$ shares $\displaystyle = 85 \times 63.25 = 5376 \text{ Rs. }$

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Question 5: A man invests Rs. 800 in buying Rs. 5 shares and when they are selling at a premium of Rs. 1.15, he sells all the shares, Find his profit and profit per cent.

Answer:

$\displaystyle \text{Number of shares bought }= \frac{800}{5} = 160$

Profit per share $\displaystyle =6.15-5 = 1.15 \text{ Rs. }$

Total investment $\displaystyle = 800 \text{ Rs. }$

Total profit $\displaystyle = 160 \times 1.15= 184 \text{ Rs. }$

$\displaystyle \text{Profit} \% = \frac{184}{800} \times 100 = 23\%$

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Question 6: Find the annual income derived from 250, Rs. 60 shares paying 5\% dividend.

Answer:

$\displaystyle \text{Dividend per share } = 60 \times \frac{5}{100} = 12 \text{ Rs. }$

Total income $\displaystyle = 250 \times 12 = 3000 \text{ Rs. }$

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Question 7: A man invests Rs. 3,072 in a company paying 5\% per annum, when its Rs. 10 share can be bought for Rs. 16 each. Find: i) His annual Income; ii) His Percentage income on his investment.

Answer:

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

$\displaystyle \text{Total number of shares bought }= \frac{3072}{16} = 192$

$\displaystyle \text{Dividend } = 192 \times 10 \times \frac{5}{100} = 96 \text{ Rs. }$

Therefore annual income $\displaystyle = 96 \text{ Rs. }$

$\displaystyle \% \text{ income on his investment }= \frac{96}{3072} \times 100 = 3.125\%$

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Question 8: A man invests Rs. 7770 in a company paying 5 per cent divided when a share of nominal value of Rs. 100 sells at a premium of Rs. 5 Find; i) The number of shares bought ii) Percentage income iii) Annual Income

Answer:

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

Cost price of the share $\displaystyle = 105 \text{ Rs. }$

$\displaystyle \text{Number of shares bought} = \frac{7770}{105} = 74$

$\displaystyle \text{Income } = 74 \times 100 \times \frac{5}{100} = 370$

$\displaystyle \text{Percentage income } = \frac{370}{7770} \times 100 = 4.76\%$

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Question 9: A man buys Rs. 50 shares of a company, paying 12 percent dividend, at a premium of Rs. 10. Find; i) The market value of 320 shares; ii) His annual income iii) His profit percent.

Answer:

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

Cost price of the share $\displaystyle = 60 \text{ Rs. }$

Market value of $\displaystyle 320$ shares $\displaystyle = 320 \times 60 = 19200 \text{ Rs. }$

$\displaystyle \text{Annual Income } = 320 \times 50 \times \frac{12}{100} = 1920 \text{ Rs. }$

$\displaystyle \text{Profit} \% = \frac{1920}{19200} \times 100 = 10\%$

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Question 10: A man buys Rs. 75 shares at a discount of Rs. 15 of a company paying 20% dividend find; i) The market value of 120 shares; ii) His annual income; ii) His profit Percent

Answer:

Nominal price of the share $\displaystyle 75 \text{ Rs. }$

Cost price of the share $\displaystyle = 75-15= 60 \text{ Rs. }$

Market value of 120 shares $\displaystyle = 120 \times 60 = 7200 \text{ Rs. }$

$\displaystyle \text{Annual Income }= 120 \times 75 \times \frac{20}{100} = 1800 \text{ Rs. }$

$\displaystyle \text{Profit} \% = \frac{1800}{7200} \times 100 = 25 \%$

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Question 11: A man has 300, Rs. 50 shares of a company paying 20% dividend. Find his net income after paying 3% income tax.

Answer:

$\displaystyle \text{Annual Income }= 300 \times 50 \times \frac{20}{100} = 3000 \text{ Rs. }$

$\displaystyle \text{Taxes paid } = \frac{3}{100} \times 3000 = 90 \text{ Rs. }$

Net Income $\displaystyle = 3000 - 90 = 2910 \text{ Rs. }$

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Question 12: A company pays a dividend of 15% on its 10 Rs. Shares from which it deducts income tax at the rate of 22%. Find the annual income of a man who owns one thousand shares of this company.

Answer:

$\displaystyle \text{Annual Income } = 1000 \times 10 \times \frac{15}{100} = 1500 \text{ Rs. }$

$\displaystyle \text{Taxes paid } = \frac{22}{100} \times 1500 = 330 \text{ Rs. }$

Net Income $\displaystyle = 1500-330 = 1170 \text{ Rs. }$

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Question 13: A man invests Rs. 8,800 in buying shares of a company of face value of Rs. 100 each at a premium of 10%. If he earns Rs. 1,200 at the end of the year as dividend. Find; i) The number of shares he has in the company. ii) The dividend percent per share. [2001]

Answer:

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

Cost price of the share $\displaystyle = 100 +10 = 110 \text{ Rs. }$

$\displaystyle \text{Number of shares bought } = \frac{8800}{110} = 80$

Dividend earned $\displaystyle = 1200 \text{ Rs. }$

Let the dividend % $\displaystyle = x$ Therefore

$\displaystyle 80 \times 100 \times \frac{x}{100} = 1200 \Rightarrow x = 15\%$

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Question 14: A man invests Rs. 1680 in buying shares of nominal value Rs. 24 and selling at 12% premium. The dividend on the shares is 15% per annum. Calculate: i) The number of shares he buys; ii) The dividend he receives. [1999]

Answer:

Nominal price of the share $\displaystyle 24 \text{ Rs. }$

$\displaystyle \text{Selling price of the share } = 24 +24 \times \frac{12}{100} = 26.88 \text{ Rs. }$

$\displaystyle \text{Number of shares bought } = \frac{1680}{26.88} = 62.5$

$\displaystyle \text{Dividend received } = 62.5 \times 24 \times \frac{15}{100} = 225 \text{ Rs. }$

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Question 15: By investing Rs. 7500 in a company paying 10% dividend, an annual income of Rs. 500 is received. What price is paid for each of Rs. 100 shares? [1990]

Answer:

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