Accessing OP Malhotra Class 10 Solutions Chapter 3 Shares and Dividends Ex 3(a) can be a valuable tool for students seeking extra practice.
S Chand Class 10 ICSE Maths Solutions Chapter 3 Shares and Dividends Ex 3(a)
Question 1.
Find the cost of
(i) 200 shares of Rs. 10 each available at Rs. 2.50 premium.
(ii) 220 shares of Rs. 15 each available at Rs. 1.50 discount.
(iii) Purchasing Rs. 200 stock yielding 9% at 105.
(iv) 1000 shares of Rs. 25 each at a premium of Rs. 60.
(v) 450 shares of Rs. 100 each at the market price of Rs. 30.80.
Solution:
(i) Face value of each share = Rs. 10
∴ Market value of each share = Rs. 10 + RS. 2.50 = Rs. 12.50
∴ Market value of 200 shares = Rs. 12.50 x 200 = Rs. 2500
(ii) Face value of each share = Rs. 15
Market value = Rs. 15 – Rs. 1.50 = Rs. 13.50
Market value of 220 shares
= Rs. 13.50 x 220 = Rs. 2970
(iii) Market value of each share = Rs. 10
∴ Market value of Rs. 200 shares
= Rs. 105 x 200 = Rs. 21000
(iv) Face value of each share = Rs. 25
Market value of each share
= Rs. 60 + 25 = Rs. 85
∴ Cost of 1000 shares = Rs. 85 x 1000
= Rs. 85000
(v) Face value of each share = Rs. 100
Market value of each share = Rs. 30.80
∴ Value of 450 shares = Rs. 30.80 x 450
= Rs. 13860
Question 2.
Find the annual dividend on
(i) 450 shares with par value of Rs. 10 if the annual dividend is 7.5%.
(ii) 50 Tata Mills 4% (Rs. 6) shares at Rs. 6.25.
(iii) 180 Shri Ram Fibres 7\(\frac { 1 }{ 2 }\)% (Rs. 10) shares at 14.50.
(iv) 100 Hindustan Motors (Rs. 10) shares at Rs. 8, dividend 4% p.a.
Solution:
(i) Face value of each share = Rs. 10
∴ Value of 450 shares = Rs. 10 x 450
= Rs. 4500
Rate of dividend = 7.5%
∴ Total dividend = 7.5% of Rs. 4500
= Rs. \(\frac{4500 \times 7.5}{100}\) = Rs. 337.50
(ii) Face value of each share = Rs. 6
∴ Value of 50 shares = Rs. 6 x 50 = Rs. 300
Rate of dividend = 4%
∴ Total dividend = 4% of Rs. 300
= Rs. 300 x \(\frac { 4 }{ 100 }\) = Rs. 12
(iii) Face value of each share = Rs. 10
∴ Value of 180 shares = Rs. 10 x 180
= Rs. 1800
Rate of dividend = 7\(\frac { 1 }{ 2 }\) % = \(\frac { 15 }{ 2 }\)%
∴ Total dividend = \(\frac { 15 }{ 2 }\) % of Rs. 1800 1800×15
= Rs. \(\frac { 1800 × 15 }{ 100 × 2 }\) = Rs. 135
(iv) Face value of each share = Rs. 10
∴ Value of 100 shares = Rs. 10 x 100
= Rs. 1000
Rate of dividend = 4%
∴ Total dividend = 4% of Rs. 1000
= Rs. 1000 x \(\frac { 4 }{ 100 }\) = Rs. 40
Question 3.
Write down the sum of money obtained by selling 60 (Rs. 100) shares at 112.
Solution:
By selling one share, money is obtained = Rs. 112
∴ By selling 60 shares, money will be obtained = Rs. 112 x 60 = Rs. 6720
Question 4.
Ravi invested Rs. 6250 in shares of a company paying 6% per annum. If he bought Rs. 25 shares for Rs. 31.25 each, find his annual income from this investment.
Solution:
By investing Rs. 31.25, shares can be purchased = 1
and by investing Rs. 6250, number of shares can be purchased = \(\frac{1 \times 6250}{31.25}\) = 200
Nominal value of 200 shares at the rate of Rs. 25 per share = Rs. 25 x 200 = Rs. 5000
Rate of dividend = 6%
Total dividend = Rs. 5000 x \(\frac { 6 }{ 100 }\) = Rs. 300
Question 5.
Write down the price of 100 (Rs. 10) shares costing Rs. 2000.
Solution:
Price of 100 shares = Rs. 2000
∴ Face value of each share
= 2000 x \(\frac { 1 }{ 100 }\) = Rs. 20
Question 6.
A company declares semi-annual dividend of 5%. Krishan Lai owns 25 shares (of par value Rs. 12.50 each). How much annual dividend must he receive.
Solution:
Face value of each share = Rs. 12.50
Value of 25 shares = Rs. 12.50 x 25 = Rs. 312.50
Rate of dividend = 5% semi annually
∴ Annually dividend = 5 x 2 = 10%
∴ Total dividend = Rs. 312.50 x \(\frac { 10 }{ 100 }\)
= Rs. 31.25
Question 7.
A man bought 250 (₹ 1) shares and received from them a dividend of ₹ 20. What is the rate % of the dividend?
Solution:
Number of shares = 250
Face value of each share = Re. 1
Total dividend = Rs. 20
Face value of 250 shares = 250 x 1 = Rs. 250
∴Rate of dividend = \(\frac{\text { Total dividend } \times 100}{\text { Total face value }}\)
= \(\frac{20 \times 100}{250}\)
Question 8.
A man invests Rs. 4800 in shares of a company which was paying 8% dividend at the time when a Rs. 100 share cost Rs. 160. Find (i) his annual income from the shares, (ii) the rate of interest he gets on his investment.
Solution:
Investment = Rs. 4800
Rate of dividend = 8%
Face value of each share = Rs. 100
Market value of each share = Rs. 160
∴Number of shares = Rs. \(\frac { 4800 }{ 160 }\) = 30
and total value of 30 shares = Rs. 100 x 30 = Rs. 3000
(i) ∴ Total dividend = Rs. \(\frac { 3000×8 }{ 100 }\) = Rs. 240
(ii) Rate of interest on his investment = \(\frac{240 \times 100}{4800}\) = 5%
Question 9.
A company pays a dividend of 15% on its ten-rupee shares from which is deducted income tax at the rate of 22%. Find the annual income of a man who owns 100 shares of this company.
Solution:
Rate of dividend = Rs. 15%
Face value of each share = Rs. 10
Rate of Income Tax = 22%
Number of shares = 100
Face value of 100 shares = Rs. 10 x 100
= Rs. 1000
∴ Total dividend = Rs. 1000 x \(\frac { 15 }{ 100 }\) = Rs. 150
Rate of Income Tax = 22%
∴ Total tax deducted = Rs. 150 x \(\frac { 22 }{ 100 }\) = Rs. 33
∴ Net annual income = Rs. 150 – Rs. 33 = Rs. 117
Question 10.
A man bought 1000 shares each of face value Rs. 5 at Rs. 7 per share. At the end of the year, the company from which he
bought the shares declared a dividend of 8%. Calculate
(i) the amount of money invested by the man;
(ii) the percentage return on his outlay correct to one decimal place.
Solution:
Number of shares = 1000
Face value of each share = Rs. 5
Market value of each share = Rs. 7
Rate of dividend = 8%
(i) Total face value of 1000 shares = Rs. 5 x 1000 = Rs. 5000
∴ Amount of investment = 1000 x Rs. 7 = Rs. 7000
(ii) Total dividend = Rs. 5000 x \(\frac { 8 }{ 100 }\) = Rs. 400
∴ Rate of interest = Rs. \(\frac{400 \times 100}{7000}\)
= \(\frac { 40 }{ 7 }\) = 5.7 %
Percentage of return = 5 \(\frac { 1 }{ 3 }\) %
Question 11.
A company with 10000 shares of nominal value Rs. 100 declares an annual dividend of 8% to the share-holders.
(i) Calculate the total amount of dividend paid by the company.
(ii) Ramesh had bought 90 shares of the company at Rs. 150 per share. Calculate the dividend he receives and the percentage return on his investment.
Solution:
Number of shares = 10000
Nominal value of each share = Rs. 100
Rate of dividend = 8%
∴ Total value of 10000 shares = Rs. 100 x 10000 = Rs. 1000000
(i) Total dividend paid by the company
= Rs. 1000000 x \(\frac { 8 }{ 100 }\) = Rs. 80000
(ii) Number of shares, Ramesh has = 90
Value of 90 shares = Rs. 100 x 90 = Rs. 9000
Dividend = Rs \(\frac{9000 \times 8}{100}\) = Rs. 720 100
Market value be each share = Rs. 150
Investment on purchasing 90 shares = Rs. 150 x 90 = Rs. 13500
Percent of interest on his investment
= Rs. \(\frac{720 \times 100}{13500}\)
= \(\frac { 16 }{ 3 }\) % = 5 \(\frac { 1 }{ 3 }\) %
Percentage of return = 5 \(\frac { 1 }{ 3 }\) %
Question 12.
Aditi has 40 shares of nominal value Rs. 100 and she decides to sell them when they are at a premium of 50%. She invests the proceeds in shares of nominal value of Rs. 75 quoted at a 20% discounts paying 25% dividend annually. Calculate:
(i) the sale proceeds
(ii) the number of shares she buys;
(iii) the annual dividend from these shares.
Solution:
Number of shares Aditi has = 40
Nominal value of each share = Rs. 100
∴ Total value of 40 shares = Rs. 100 x 40 = Rs. 4000
Market price of each shares = Rs. 100 + 50 = Rs. 150
(i) Amount received on selling them = Rs. 150 x 40 = Rs. 6000
(ii) In second case, nominal value of each share = Rs. 75
Market value of each share 20% discount
= Rs. \(\frac{75 \times(100-20)}{100}\) = Rs. \(\frac{75 \times 80}{100}\)
= Rs. 60
Rate of dividend = 25% annually
(i) Number of shares be bought
= Rs. \(\frac { 6000 }{ 60 }\) = 100
(ii) Face value of 100 shares at the rate of Rs. 75 = 75 x 100
(iii) Annual dividend = Rs. \(\frac{7500 \times 25}{100}\) = Rs. 1875
Question 13.
Mr. Khanna holds 1600, Rs. 100 shares of a company that pays 12% dividend annually. Calculate his annual dividend. If he had bought these shares at 50% premium, what percentage return does he get on his investment.
Solution:
Number of shares Mr. Khanna holds = 1600
Face value of each share = Rs. 100
Annually dividend = 12%
(i) Total value of 1600 shares = Rs. 100 x 1600 = Rs. 160000
and total dividend = Rs. \(\frac{160000 \times 12}{100}\)
= Rs. 19200
Cost price of each share = Rs. 100 + 50 = Rs. 150
Total investment = 1600 x 150 = Rs. 240000
∴ Percentage of return will be
= \(\frac{19200 \times 100}{240000}\)
Question 14.
A man invests Rs. 11200 in a company paying 6% dividend per annum when its Rs. 100 shares can be bought for Rs. 140. Find (i) his annual dividend, (ii) his percentage income on this investment.
Solution:
Total investment = Rs. 11200
Rate of dividend = 6%
Face value of each share = Rs. 100
and market value = Rs. 140
∴ Number of shares purchased
= RS. \(\frac { 11200 }{ 140 }\)
Face value of 80 shares = Rs. 100 x 80 = Rs. 8000
(i) Annual dividend = Rs. 8000 x \(\frac { 6 }{ 100 }\) = Rs. 480
(ii) Percentage income on his investment
= Rs. \(\frac{480 \times 100}{11200}\) = \(\frac { 30 }{ 7 }\) = 4\(\frac { 2 }{ 7 }\) % p.a.
Question 15.
A company having a capital stock of Rs. 450000 declares a dividend of 4% semi-annually.
(a) What is the annual income of a stockholder owning 135 shares at par- value of Rs. 10?
(b) What is the total amount of dividend paid annually by the company?
Solution:
Total capital stock = Rs. 450000
Rate of dividend = 4% semi annually or 4 x 2 = 8% annually
(a) Number of shares = 135
Nominal value of each share = Rs. 10
∴ Total value of 135 shares = Rs. 10 x 135 = Rs. 1350
Dividend of Rs. 1350 = Rs. 1350 x \(\frac { 8 }{ 100 }\) = Rs. 108
(b) Total amount of dividend annually 8
= Rs. 450000 x \(\frac { 8 }{ 100 }\)
= Rs. 36000