The availability of step-by-step OP Malhotra Class 10 Solutions Chapter 3 Shares and Dividends Ex 3(b) can make challenging problems more manageable.
S Chand Class 10 ICSE Maths Solutions Chapter 3 Shares and Dividends Ex 3(a)
Question 1.
Find the number of shares that can be bought and the income obtained by investing :
(a) Rs. 50 in (Re. 1) shares at Rs. 1.25 paying 8%.
(b) Rs. 240 in (Rs. 5) shares at Rs. 8, paying 9%.
Solution:
(a) Investment = Rs. 50
Face value of each share = Re. 1
Market value = Rs. 1.25
Rate of dividend = 8%
∴ Number of shares = \(\frac { 50 }{ 1.25 }\) = \(\frac{50 \times 100}{125}\)
= 40 shares
Face value of 40 shares = 40 x Re. 1 = Rs. 40
= Rs. \(\frac { 320 }{ 100 }\) = Rs. 3.20
(b) Investment = Rs. 240
Face value of each share = Rs. 5
and market value = Rs. 8
Rate of dividend = 9%
∴ Number of shares = Rs. \(\frac { 240 }{ 8 }\) = 30
Face value of 30 shares = 30 x 5 = Rs. 150
Amount of dividend = Rs. \(\frac{150 \times 9}{100}\)
= Rs. \(\frac { 1350 }{ 100 }\)
= Rs. 13.50
Question 2.
A man bought 160 (Rs. 5) shares for Rs. 360. At what price did the shares stand? At what premium or discount were they quoted?
Solution:
Number of shares = 160
Face value of each share = Rs. 5
Amount of 160 shares = Rs. 360
∴ Market value of each share = Rs.\(\frac {360}{160}\)
= Rs. \(\frac {9}{4}\) = Rs. 2.25 4
Difference of values of each share
= Rs. 5.00 – Rs. 2.25 = Rs. 2.75
∴ Market value is less than the face value
∴ The shares were quoted Rs. 2.75 at discount
Question 3.
A man sold 600 (Re. 1) shares for Rs. 750. At what price did the shares stand? At what premium or discount were they quoted?
Solution:
Number of shares = 600
Face value of each share = Re. 1
Total market value of 600 shares = Rs. 750
∴ Market value of each share = Rs. \(\frac {750}{600}\)
= Rs. \(\frac {5}{4}\) = Rs. 1.25
Difference of values of each share = Rs. 1.25. – 1.00 = 0.25
Difference of the values of each shares = Rs. 1.25 – 1.00 = 0.25
∵ Market value of each share is more than its face value
∴ The shares were quoted Rs. 0.25 at premium
Question 4.
A man buys 200 ten rupee shares at Rs. 12.50 each and receives a dividend of 8%. Find the amount invested by him and dividend received by him in cash.
Solution:
Number of shares bought = 200
Face value of each share = Rs. 10
Market value = Rs. 12.50
Rate of dividend = 8%
∴ Total amount of investment = Rs. 12.50 x 200 = Rs. 2500
and amount of face value = Rs. 10 x 200 = Rs. 2000
∴ Dividend = Rs. 2000 x \(\frac {8}{100}\) = Rs. 160
Question 5.
A man bought 500 shares, each of face value Rs. 10 of a certain business concern and during the first year after purchase received Rs. 400 as dividend on his shares. Find the rate of dividend on his shares.
Solution:
Number of shares bought = 500
Nominal value of each share = Rs. 10
Amount of dividend = Rs. 400
Total nominal value of 500 shares = Rs. 10 x 500 = Rs. 5000
∴ Dividend on Rs. 5000 = Rs. 400
and dividend on Rs. 100 = \(\frac{400 \times 100}{5000}\) = 8%
Question 6.
By purchasing ₹ 25 shares for ₹ 40 each a man gets 4 per cent profit on his investment. What rate per cent is the company paying? What is his dividend if he buys 60 shares ?
Solution:
Face value of each share = Rs. 25
Market value = Rs. 40
Profit = 4%
Profit on Rs. 25 = Rs. 4
∴ Profit on Rs. 40 = \(\frac{4 \times 40}{25}=\frac{32}{5}\) = 6.4
∴ Rate of dividend = 6.4%
Face value of 60 shares = Rs. 25 x 60 = Rs. 1500
∴ Dividend on Rs. 1500 = Rs. 1500 x \(\frac { 6.4 }{ 100 }\) = Rs. 96.0 = Rs. 96
Question 7.
Mukul invests Rs. 9000 in a company paying a dividend of 6% per annum when a share of face value 100 stands at Rs. 150. What his annual income? He sells 50% of his shares when the price rises to Rs. 200. What is his gain on this transaction?
Solution:
Investment of Mukul = Rs. 9000
Rate of dividend = 6% p.a.
Face value of each share = Rs. 100
and market value = Rs. 150
∴ Number of shares = Rs. \(\frac { 9000 }{ 150 }\) = 60
Face value of 60 shares = Rs. 100 x 60 = Rs. 6000
∴ Amount of annual dividend = Rs. \(\frac{6000 \times 6}{100}\) = Rs. 360
50% of shares which were sold = 60 x \(\frac { 50 }{ 100 }\) = 30
Market value of each share = Rs. 200
∴ Amount received = Rs. 200 x 30 = Rs. 6000
and market value of remaining 30 shares = Rs. 150 x 30 = Rs. 4500
Total amount received = Rs. 6000 + 4500 = Rs. 10500
∴ Total profit = Rs. 10500 – 9000 = Rs. 1500
Question 8.
By investing Rs. 7500 in a company paying 10% dividend, an income of Rs. 500 is received. What price is paid for each Rs. 100 share? Solution:
Investment = Rs. 7500
Rate of dividend = 10%
Total income = Rs. 500
Face value of each share = Rs. 100
∴ Total face value of shares = Rs \(\frac{500 \times 100}{10}\) = Rs. 5000
∴ Number of shares = Rs. \(\frac{5000}{100}\) = 50
Now market value of 50 share; = Rs. 7500
∴ Market value of each share
= Rs. \(\frac { 7500 }{ 500 }\) = Rs. 150
Question 9.
Arun owns 560 shares of a company. The face value of each share is Rs. 25. The company declares a dividend of 9%. Calculate:
(i) the dividend Arun would receive, and
(ii) the rate of interest, on his investment. Considering that Arun bought these shares @ ₹30 per share in the market.
Solution:
Number of shares Arun has = 560
Face value of each share = ₹ 25
Rate of dividend = 9%
Now total face value of 560 shares = ₹ 25 x ₹ 60 = ₹ 14000
(i) Total dividend received by Arun
= ₹ \(\frac{14000 \times 9}{100}\) = ₹ 1260
(ii) Market value of each share = ₹ 30
Total investment = ₹ 30 x 560 = ₹ 16800
Rate of interest on the investment
= ₹ \(\frac{1260 \times 100}{16800}\)
= 7.5% or 7\(\frac { 1 }{ 2 }\)%
Question 10.
What sum should Ashok invest in ₹ 25 shares selling at ₹36 to obtain an income of ₹720, if the dividend declared is 12%. Also find :
(i) the number of shares bought by Ashok.
(ii) the percentage return on his investment.
Solution:
Face value of each share = ₹ 25
Market value = ₹ 36
Total income = ₹ 720
(i) Rate of dividend = 12%
∴ Face value of shares = \(\frac{720 \times 100}{12}\) = ₹ 6000
and number of shares = ₹ \(\frac { 6000 }{ 25 }\) = 240
Investment by Ashok = 240 x ₹ 36 = ₹ 8640
Percentage of return = ₹ \(\frac{720 \times 100}{8640}\)
= \(\frac { 25 }{ 3 }\) = 8\(\frac { 1 }{ 2 }\)% = 8.33%
Question 11.
Mr. Sharma has 60 shares of nominal value 7100 and he decides to sell them when they are at a premium of 60%. He invests the proceeds in shares of nominal value ₹ 50, quoted at 4% discount, paying 18% dividend annually. Calculate:
(i) the sale proceeds.
(ii) the number of shares he buys.
(iii) the annual dividend from these shares.
Solution:
Number of shares = 60
Face value of each share = ₹ 100
Market value = 60% premium = ₹ 100 + 60 = ₹ 160
(i) Sale proceed = ₹ 160 x 60 = ₹ 9600
(ii) Nominal value of share purchased = ₹ 50
Market value as quoted 4% discount
= ₹ 50 – \(\frac { 50×4 }{ 100 }\)
= ₹ 50 – 2 = ₹ 48
∴ Number of shares purchased = \(\frac { 9600 }{ 48 }\) = 200
(iii) Rate of dividend = 18% p.a.
Face value of 200 shares = ₹ 50 x 200 = ₹ 10000
∴ Annual dividend = ₹ 10000 x \(\frac { 18 }{ 100 }\) = ₹ 1800
Question 12.
A man invests a sum of money in ₹ 100 shares, paying 15% dividend, quoted at 20% premium. If his annual dividend is ₹ 540, calculate:
(i) his total investment.
(ii) the rate of return on his investment.
Solution:
Rate of dividend = 15% at 20% premium
Annual dividend = ₹ 540
∴ Investment = ₹ \(\frac{540 \times(100+20)}{15}\)
= ₹ \(\frac{540 \times 120}{15}\) = ₹ 4320
and rate of returns on his investment
= \(\frac{540 \times 100}{4320}\) = \(\frac { 100 }{ 8 }\)% = 12.5 %
Question 13.
A lady holds 1800 hundred rupee shares of a company that pays 15% dividend annually. Calculate her annual dividend. If she had bought these shares at 40% premium, what percentage return would she have got on her investment? Give your answer to the nearet integer.
Solution:
Number of shares = 1800
Face value of each share = ₹ 100
Dividend rate = 15%
Market value of each share = ₹ 100 + ₹ 40 = ₹ 140
(i) ∴ Annual dividend = ₹ 1800 x 15 = ₹ 27000
(ii) Investment = ₹ 1800 x 140 = ₹ 252000
∴ Percentage return = \(\frac{27000 \times 100}{252000}\)
= \(\frac { 75 }{ 7 }\) % = 10 \(\frac { 5 }{ 7 }\) % = 11%
Question 14.
A man invests ₹ 11200 in a company paying 6% dividend when its ₹ 100 share can be bought for ₹ 140. Find:
(i) his annual income.
(ii) the percentage income on his investment.
Solution:
Investment = ₹ 11200
Rate of dividend = 6%
Face value of each share = ₹ 100
Market value of each share = ₹ 140
(i) Annual income = ₹ \(\frac{11200 \times 6}{140}\) = ₹ 480
(ii) Percentage income on his investment
= \(\frac{480 \times 100}{11200} \%=\frac{30}{7} \%=4 \frac{2}{7} \%\)
Question 15.
A company with 10,000 shares of 7100 each, declares an annual dividend of 5%.
(i) What is the total amount of dividend paid by the company?
(ii) What would be the annual income of a man, who has 72 shares in the company?
(iii) If he received only 4% of his investment, find the price he had paid for each share.
Solution:
Number of share with a company = 10000
Face value of each share = ₹ 100
Rate of annual dividend = 5%
(i) Total dividend = 10000 x 5 = ₹ 50,000
(ii) Income on 72 shares = 72 x ₹ 5 = ₹ 360
(iii) Rate of returns he receives = 4%
∴ Market value of two shares
= \(\frac{\text { Dividend } \times 100}{4}\)
= \(\frac{50,000 \times 100}{4}\)
= ₹ 1250000
Market value of each share
= ₹ \(\frac {1250000}{10000}\) = ₹ 125
Question 16.
A man invest ₹ 1680 in buying shares of nominal value ₹ 24 and selling at 12% premium. The dividend on the shares is 15% per annum.
(i) Calculate the number of shares he buys.
(ii) Calculate the dividend he receives annually. (ICSE 1999)
Solution:
Investment = ₹ 1680
Nominal value of each share = ₹ 24
and market value = ₹ 24 x \(\frac {112}{100}\) = \(\frac {2688}{100}\)
= ₹ 26.88
∴ Number of shares = \(\frac {1680}{26.88}\)
= \(\frac{1680 \times 100}{2688}\) = \(\frac {125}{2}\) shares
= 62.5 shares
Rate of dividend = 15%
Market value of each share = ₹ 100 + ₹ 12
= ₹ 112
Dividend = \(\frac{1680 \times 15}{112}\) = ₹ 225
Question 17.
A man invests ₹ 7425 on buying share of face value ₹ 90 each at a premium of 10% in a company. If he at a earns ₹ 1350 as dividend at the end of the year, find
(i) the number of shares he has in the company.
(ii) the dividend percentage per share that he received.
Solution:
Amount of dividend = ₹ 1350
Investment = ₹ 7425
Face value of each share = ₹ 90
Market value = at premium of 10%
= ₹ \(\frac{90 \times(100+10)}{100}\)
= ₹ \(\frac{90 \times 110}{100}\) = ₹ 99
(i) ∴ Number of shares = \(\frac {7425}{99}\) = 75
and face value of 75 shares = 75 x ₹ 99
= ₹ 6750
(ii) Rate of dividend = \(\frac{1350 \times 100}{6750}\) = 20%
Question 18.
Abhisheksold a certain number of shares of ₹ 20 paying 8% dividend at ₹ 18 and invested the proceeds in ₹ 10 shares, paying 12% dividend at 50% premium. If the change in his annual income is ₹ 120, find the number of shares sold by him ?
Solution:
In first case,
Face value of each share = ₹ 20
Rate of dividend = 8%
Market value of each share = ₹ 18
Let number of shares = x
∴ Sale proceed by selling x shares = ₹ 18 × x = ₹ 18x
and Face value of x shares = ₹ x × 20 = ₹ 20x
∴ Dividend = 20x × \(\frac { 8 }{ 100 }\) = ₹ \(\frac { 8 }{ 5 }\) x
In second case
Face value of each share = ₹ 10
Market value 50% at premium
= ₹ \(\frac{10 \times(100+50)}{100}=₹ \frac{10 \times 150}{100}\) = ₹ 15
Rate of dividend = 12%
Number of shares purchased = \(\frac { 18x }{ 15 }\) = \(\frac { 6 }{ 5 }\)x
Now face value of each shares = \(\frac { 6 }{ 5 }\)x × 10 = ₹ 12 x
Dividend = ₹ 12x × \(\frac { 12 }{ 100 }\) = ₹ \(\frac { 36 }{ 25 }\)x
Difference in dividend = \(\frac { 8 }{ 5 }\)x – \(\frac { 36 }{ 25 }\)x
= \(\frac{40 x-36 x}{25}\) = \(\frac { 4 }{ 25 }\)x
But actual difference of dividend = ₹ 120
∴ \(\frac { 4 }{ 25 }\)x = 120
x = \(\frac{120 \times 25}{4}\) = 750
∴ Number of shares = 750
Question 19.
A person invested ₹ 8000 and ₹ 10000 in buying shares of two companies which later on declared dividends of 12% and 8% respectively. He collects the dividends and sells out his shares at a loss of 2% and 3% respectively. Find his total earning from the above transaction.
Solution:
In first case, investment = ₹ 8000
Rate of dividend = 12%
∴ Income = ₹ \(\frac{8000 \times 12}{100}\) = ₹ 960
In second case, investment = ₹ 10000
Rate of dividend = 8%
∴ Income = ₹ \(\frac{1000 \times 8}{100}\) = ₹ 800
Total income = ₹ 960 + 800 = ₹ 1760
Total loss = ₹ \(\left(8000 \times \frac{2}{100}+10000 \times \frac{3}{100}\right)\) = ₹ 800
= ₹ 160 + ₹ 300 = ₹ 460
∴ Net gain = Total income – Loss
= ₹ 1760 – 460 = ₹ 1300
Question 20.
A person invested 20%, 30% and 25% of his savings in buying shares of three different companies A, B and C, which declared dividends of 10%, 12% and 15% respectively. If his total income on account of dividends be ₹ 2337.50, find his saving and the amount which he invested in buying shares of each company.
Solution:
Let the total savings = ₹ x
Investment in A Company = \(\frac { 20 }{ 100 }\) × x = \(\frac { x }{ 5 }\)
Investment in B Company = \(\frac { 30 }{ 100 }\) × x = \(\frac { 3 }{ 10 }\)x
and investment in C Company = \(\frac { 25 }{ 100 }\) × x = \(\frac { x }{ 4 }\)
Now income from A Company = \(\frac { x }{ 5 }\) x \(\frac { 10 }{ 100 }\)
= ₹ \(\frac { x }{ 50 }\)
Income from B Company = \(\frac { 3 }{ 10 }\)x × \(\frac { 12 }{ 1o0 }\)
= ₹ \(\frac { 9 }{ 250 }\)x
and income from C Company = \(\frac { x }{ 4 }\) x \(\frac { 15 }{ 100 }\)
= ₹ \(\frac { 3x }{ 80 }\)x
∴ Total inccme = \(\frac{x}{50}+\frac{9}{250} x+\frac{3 x}{80}\)
= \(\frac{40 x+72 x+75 x}{2000}=\frac{187}{2000}\)x
But total income = ₹ 2337.50
∴ \(\frac{187}{2000} x=2337.50 \Rightarrow x=\frac{233750 \times 2000}{100 \times 187}\)
⇒ x = 25000
∴ Total investment = ₹ 25000
Now investment in A Company
= ₹ 25000 x \(\frac { 20 }{ 100 }\) = ₹ 5000
Investment in B Company
= ₹ 25000 x \(\frac { 30 }{ 100 }\) = ₹ 7500
and investment in C Company
= ₹ 25000 x \(\frac { 25 }{ 100 }\) = ₹ 6250
Self Evaluation And Revision (Latest ICSE Questions)
Question 1.
A dividend of 9% was declared on ₹ 100 shares selling at a certain price. If the rate of return is 7\(\frac { 1 }{ 2 }\)%, calculate :
(i) the market value of the share
(ii) the amount to be invested to obtain an annual dividend of ₹ 630.
Solution:
Market price of each share = x
Face value of each share = ₹ 100
Rate of dividend = 9%
Rate of return on investment = 7\(\frac { 1 }{ 2 }\)% = \(\frac { 15 }{ 2 }\)%
(i) ∴ \(\frac{x \times 15}{100 \times 2}\) = 9 ⇒ x = \(\frac{9 \times 100 \times 2}{15}\) = ₹ 120
∴ Market value of each share = ₹ 120
(ii) Amount of dividend = ₹ 630
∴ Investment = \(\frac{630 \times 100}{\frac{15}{2}}\) = \(\frac{630 \times 100 \times 2}{15}\)
= ₹ 42 x 2 x 100 = ₹ 8400
Question 2.
A man invests ₹ 8800 in buying shares of face value of rupees hundred each at a premium of 10% in a company. If he earns ₹ 1200 at the end of the year as dividend, find
(i) the number of shares he has in the company ?
(ii) the dividend percentage per share.
Solution:
Investment = ₹ 8800
Face value of each share = ₹ 1100
Market value at a premium of 10%
= ₹ 100 + 10 = ₹ 110
Total dividend he received = ₹ 1200
(i ) Number of shares = \(\frac{\text { Investment }}{\mathrm{MV}}\)
= \(\frac { 8800 }{ 110 }\) = 80
(ii) Face value of each share = ₹ 100 x 80 = ₹ 8000
∴ Rate of dividend per share = \(\frac { 1200 }{ 8000 }\) x 100
= 15%
Question 3.
A man wants to buy 62 shares available at ₹ 132 (par value of ₹ 100).
(i) How much should he invest ₹
(ii) If the dividend is 7.5%, what will be his annual income?
(iii) If he wants to increase income by ₹ 150, how many extra shares should he buy?
Solution:
Number of shares = 62
Market value of each share = ₹ 132
Face value = ₹ 100
(i) His investment = ₹ 132 x 62 = ₹ 8184
(ii) Rate of dividend = 7.5% = \(\frac { 15 }{ 2 }\) % p.a.
Annual income = ₹ 62 x 100 x \(\frac { 15 }{ 2×100 }\)
= ₹ 465
(iii) Extra income he wants = ₹ 150
Then annual income = ₹ 465 + 150 = ₹ 615
∴ Number of shares = \(\frac{615 \times 100 \times 2}{15 \times 100}\) = 82
∴ Extra share he has to buy = 82 – 62 = 20
Question 4.
A man invests ₹ 20,020 in buying shares of nominal value ₹ 26 at 10% premium. The dividend on the shares is 15% per annum. Calculate :
(i) The number of shares he buys.
(ii) The dividend he receives annually.
(iii) The rate of interest he gets on his money.
Solution:
Investment = ₹ 20020
Nominal value of each share = ₹ 26
Market value at 10% premium
= ₹ \(\frac{26 \times(100+10)}{100}\)
= ₹ \(\frac{26 \times 110}{100}\) = ₹ \(\frac { 2860 }{ 100 }\) = ₹ 28.60
Rate of dividend = 15%
(i) Number of share he bought = \(\frac { 20020 }{ 28.60 }\)
= \(\frac{20020 \times 100}{2860}\) = 70
(ii) Total dividend per year = 700 x 26 x 15%
= \(\frac{700 \times 26 \times 15}{100}\) = ₹ 2730
(iii) Rate of interest on investment
= \(\frac{2730 \times 100}{20020}\) = 13.636 %
= 13.46%
Question 5.
A man invested ₹ 45,000 in 15% ₹ 100 shares quoted at ₹ 125. When the market value of these shares rose to ₹ 140, he sold some shares, just enough to raise ₹ 8400. Calculate :
(i) the number of shares he still holds;
(ii) the dividend due to him on these remaining shares.
Solution:
Total investment = ₹ 45000
Face value of each share = ₹ 100
Market value = ₹ 125
Rate of dividend = 15%
∴ Number of shares = \(\frac { 4500 }{ 125 }\)
He sells some shares at the rate of ₹ 140
(i) Raise his income ₹ 8400
∴ Number of shares he sells = \(\frac { 8400 }{ 140 }\) = 60
Remaining shares = 360 – 60 = 300
Dividend on remaining shares = 300 x 100 x 15%
= ₹ \(\\frac{300 \times 100 \times 15}{100}\) = ₹ 4500
Question 6.
Mr. Tewari invested ₹ 29,040 in 15%, ₹ 100 shares quoted at a premium of 20%. Calculate :
(i) The number of shares bought by Mr. Tewari.
(ii) Mr. Tewari’s income from the investment.
(iii) The percentage return on his investment.
Solution:
Investment made by Tewari = ₹ 29040
Face value of each share = ₹ 100
Market value at a premium of 20%
= ₹ 100 + 20 = ₹ 120
Rate of dividend = 15%
(i) Number of shares bought = ₹ \(\frac { 29040 }{ 120 }\) = 242
(ii) Income from investment = ₹ 242 x 100 x 15%
= ₹ 242 x 100 x \(\frac { 15 }{ 100 }\) = ₹ 3630
(iii) Percentage income on investment
= ₹ \(\frac{3630 \times 100}{29040}\) = 12.5%
Question 7.
Mr. Ram Gopal invested ₹ 8000 in 7% ₹ 100 shares at ₹ 80. After a year he sold these shares at ₹ 75 each and invested the proceeds (including his dividend) in 18%, ₹ 25 shares at ₹ 41. Find :
(i) his dividend for the first year.
(ii) his annual income in the second year.
(iii) the percentage increase in his return on his original investment.
Solution:
Investment made by Ram Gopal = ₹ 8000
Face value of each share = ₹ 100
Market value = ₹ 80
Rate of dividend = 7%
Number of shares = ₹ \(\frac { 8000 }{ 80 }\) = 100
(i) Dividend for the first year = ₹ 100 x 100 x 7%
= \(\frac{100 \times 100 \times 7}{100}\) = ₹ 700
(ii) M.V. of second year = ₹ 75
∴ Sale proceed = ₹ 100 x 75 = ₹ 7500
Total investment including dividend = ₹ 7500 + 700 = ₹ 8200
Rate of dividend in second year = 18%
M.V. = ₹ 41
Face value = ₹ 25
∴ Number of shares bought = \(\frac { 8200 }{ 41 }\) = 200
Nominal value of 200 share = ₹ 25 x 200 = ₹ 5000
∴ Dividend = ₹ 5000 x 18%
= ₹ 5000 x \(\frac { 18 }{ 100 }\) = ₹ 900
(iii) Increase in income = ₹ 900 – ₹ 700 = ₹ 200
∴ Increase percent = \(\frac{200 \times 100}{8000}\)
= \(\frac { 5 }{ 2 }\) % = 2.5%
Question 8.
Ajay owns 560 shares of a company. The face value of each share is ₹ 25. The company declares a dividend of 9%. Calculate :
(i) The dividend that Ajay will get.
(ii) The rate of interest on his investment, if Ajay had paid ₹ 30 for each share.
Solution:
Ajay has shares of a company = 560
Face value of each share = ₹ 25
Rate of dividend = 9%
(i) Face value of 560 shares = ₹ 25 x 560
= 114000
∴ Total dividend he received
= ₹ 14000 x 9%
= ₹ 14000 x \(\frac { 9 }{ 100 }\) = ₹ 1260
(ii) M.V. of each share = ₹ 30
∴ Total investment = ₹ 30 x 560 = ₹ 16800
Rate of interest on his investment = \(\frac{1260 \times 100}{16800}\) = 7.5 %
Question 9.
A company with 4000 shares of nominal value of ₹ 110 each declares an annual dividend of 15%. Calculate:
(i) The total amount of dividend paid by the company.
(ii) The annual income of Shah Rukh who holds 88 shares in the company.
(iii) If he received only 10% on his investment, find the price Shah Rukh paid for each share.
Solution:
Number of shares = 4000
Nominal value of each share = ₹ 110
Rate of dividend = 15%
(i) ∴ Total amount of dividend
= ₹ 4000 x 110 x 15%
= ₹ \(\frac{4000 \times 110 \times 15}{100}\)
= ₹ 66000
(ii) Face of 88 shares = ₹ 110 x 88 = ₹ 9680
∴ Annual income of Shah Rukh
= ₹ \(\frac { 9680×15 }{ 100 }\) = ₹ 1452
(iii) Interest on investment made by Shah Rukh = 10%
∴ Price (value) of each share paid by Shah
Question 10.
Amit Kumar invests ₹ 36,000 in buying ₹ 100 shares at ₹ 10 premium. The dividend is 15% per annum. Find
(i) the number of shares he buys.
(ii) his yearly dividend.
(iii) the percentage return on his investment.
Give your answer correct to the nearest whole number.
Solution:
Investment = ₹ 36000
Face value = ₹ 100
Premium = ₹ 20, dividend = 15%
(i) No. of shares = \(\frac { 36000 }{ 120 }\) = 300
(ii) Dividend = 15% of (100 x 300)
= \(\frac { 15 }{ 100 }\) x 30000 = ₹ 4500
(iii) Per cent of return on investment
= \(\frac { 45000 }{ 36000 }\) x 100 = \(\frac { 450 }{ 36 }\) = 12.5% = 13%
Question 11.
Vivek invests ₹ 4,500 in 8% ₹ 10 shares at ₹ 15. He sells the shares when the price rises to ₹ 30, and invests the proceeds in 12% ₹ 100 shares at ₹ 125. Calculate.
(i) the sale proceeds,
(ii) the number of ₹ 125 shares he buys,
(iii) the change in his annual income from dividend.
Solution:
(i) If price of share bought is ₹ 15, then face value of share = Rs. 10
If price of share bought is ₹ 4500, then face value of share bought
= \(\frac { 10 }{ 15 }\) x 4500 = ₹ 3000
Total face value of ₹ 10 shares = ₹ 3000 Income = 8%
= \(\frac { 8 }{ 100 }\) x 3000 = Rs. 240
By selling ₹ 10 share money received = ₹ 30
By selling Rs. 3000 shares money
= \(\frac { 30 }{ 10 }\) x 3000 = ₹ 9000
(ii) By investing ₹ 125, no. of share of ₹ 100 bought = 1
By investing ₹ 9000, no. of share of ₹ 100 bought = \(\frac { 1 }{ 125 }\) x 9000 = 72
∴ No. of ₹ 125 shares bought = 72
(iii) By investing ₹ 125 in ₹ 100 share, income = ₹ 12
By investing Rs. 9000 in ₹ 100 share, income 12
= \(\frac { 12 }{ 125 }\) x 9000 = ₹ 864
Increase in income = ₹ 864 – ₹ 240 = ₹ 624
Question 12.
Mr. Parekh invested ₹ 52,000 on ₹ 100 shares at a discount of ₹ 20 paying 8% dividend. At the end of one year he sells the shares at a premium of ₹ 20. Find :
(i) The annual dividend.
(ii) The profit earned including his dividend.
Solution:
Investment = ₹ 52000
Face value of 1 share = ₹ 100
Market value of 1 share = ₹ 100 – 20 = ₹ 80
No. of shares = \(\frac { 52000 }{ 80 }\) = 650
(i) Annual dividend = \(\frac { 8 }{ 100 }\) x 650 x 100 = ₹ 5200
(ii) S.P. of 1 share = ₹ 100 + 20 = ₹ 120
S.P. of 650 shares = ₹ 120 x 650 = ₹ 78000
C.P. of 650 shares = ₹ 100 x 650 = ₹ 65000
Profit = S.P. – C.P.
= ₹ 78000 – ₹ 52000 = ₹ 26000
Profit including dividend = ₹ 26000 + ₹ 5200 = ₹ 31200
Question 13.
A man invests ₹ 9600 on ₹ 100 shares at ₹ 80. If the company pays him 18% dividend, find :
(i) the number of shares he buys.
(ii) his total dividend.
(iii) his percentage return on the shares.
Solution:
Amount of investment = ₹ 9600
Price of one share = ₹ 80
(i) ∴ No. of shares bought = ₹ \(\frac { 9600 }{ 80 }\) = 120
(ii) Face value of 120 shares = ₹ 120 x 100 = ₹ 12000
Rate of dividend = 18%
Dividend = ₹ \(\frac { 12,000×18 }{ 100 }\) = ₹ 2160
(iii) By investing ₹ 9600, returned obtained = ₹ 2160
So, percentage return = \(\frac{2.160 \times 100}{9600}\) = 22.5%
Question 14.
Salman buys 50 shares of face value ₹ 100 available at ₹ 7132.
(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 ₹ 150, how many extra shares should he buy?
Solution:
F.V. = ₹ 100
(i) M.V. = ₹ 132, no. of shares = 50
Investment = no. of shares x MV.
= 50 x 132 = ₹ 6600
(ii) Income per share = 7.5% of F.V.
= \(\frac { 75 }{ 10×100 }\) x 100 = ₹ 7.5
∴ Annual income = 7.5 x 50 = ₹ 375
(iii) New annual income = 375 + 150 = ₹ 525
∴ No. of shares = \(\frac { 525 }{ 7.5 }\) = 70
∴ No. of extra share = 70 – 50 = 20
Question 15.
Salman invests a sum of money in ₹ 50 shares, paying 15% dividend quoted at 20% premium. If his annual dividend is ₹ 600, calculate:
(i) the number of shares he bought.
(ii) his total investment.
(iii) the rate of return on his investment.
Solution:
Nominal value = ₹ 50
Dividend on 1 share = \(\frac { 15 }{ 100 }\) x ₹ 50 = ₹ 7.50
Total Dividend to Salman = ₹ 600
(i) No. of shares Salman bought = \(\frac { 600 }{ 7.50 }\)
= \(\frac{600 \times 100}{750}\) = 80
(ii) Premium on 1 share = 50 x \(\frac { 20 }{ 100 }\) = ₹ 10
Market value of 1 share = 50 + 10 = ₹ 60
Total investment for 80 shares = 80 x 60 = ₹ 4800
(iii) Rate of return = \(\frac{\text { Total dividend }}{\text { Total investment } \times 100}\)
= \(\frac { 600 }{ 4800 }\) x 100 = 12.5%
Question 16.
Rohit invested ₹ 9,600 on ₹ 100 shares at ₹ 20 premium paying 8% dividend. Rohit sold the shares when the price rose to ₹ 160. He invested the proceeds (excluding dividend) in 10% ₹ 50 shares at ₹ 40. Find the:
(i) original number of shares.
(ii) sale proceeds.
(iii) new number of shares.
(iv) change in the two dividends.
Solution:
(i) 100 shares at ₹ 20 premium means
Nominal value of the share is ₹ 100
and its marked value = 100 + 20 = ₹ 120
Money required to buy 1 share = ₹ 120
Number of shares
= \(\frac{\text { Money invested }}{\text { Market value of } 1 \text { share }}\)
= \(\frac { 9600 }{ 120 }\) = 80 shares
(ii) Dividend on 1 share = 8% of N.V.
= 8% of 100 = 8
Total dividend on 80 shares = 80 x 8 = ₹ 640
Each share is sold at ₹ 160
∴ The sale proceeds = 80 x ₹ 160
= ₹ 12800
(iii) New investment = ₹ 12800
Divident=10%
Net value = 50
Market value = ₹ 40
∴ Number of shares = \(\frac{\text { Investment }}{\text { Market value }}\)
= \(\frac { 12800 }{ 40 }\)
= 340 shares
(iv) Now, dividend on 1 share = 10% of N.V.
= 10% of 50 = 5
∴ Dividend on 340 shares = 1600
Change in two dividends = ₹ 1600 – ₹ 640 = ₹ 960
Question 17.
Ashok invested ₹ 26,400 on 12%, ₹ 25 shares of a company. If he receives a dividend of ₹ 2,475. Find the :
(i) number of shares he bought.
(ii) market value of each share.
Solution:
Investment = ₹ 26400
Rate of divident = 12%
Divident = ₹ 2475
Face value of one share = ₹ 25
Total dividend = Number of shares x Rate of dividend x Face value of one share
2475 = Number of shares x \(\frac { 12 }{ 100 }\) x 25
Number of shares = \(\frac { 2475 }{ 3 }\) = 825
Market value of one share Investment
= \(\frac{\text { Investment }}{\text { Number of shares bought }}\)
Market value of one share = \(\frac { 26400 }{ 825 }\) = ₹ 32
Ashok bought 825 shares and market value of each share is ₹ 32.