Exercise : Chapter 3 Shares and Dividends Exercise 3C MCQ Questions and Answers
1. By investing ₹ 45,000 in 10% ₹ 100 shares, Sharad gets ₹ 3,000 as dividend. Find the market value of each share.
Solution :
Annual income from 1 share = 10% of ₹ 100 = ₹ 10
Total annual income = ₹ 3000
∴ Number of shares bought = (Total annual income / Annual income from 1 share) = 3000/10 = 300
⇒ Market value of one share = (Total investment/Number of shares) = 45000/300 = ₹ 150
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2. Mrs. Kulkarni invests ₹ 1, 31,040 in buying ₹ 100 shares at a discount of 9%. She sells shares worth ₹ 72,000 at a premium of 10% and the rest at a discount of 5%. Find her total gain or loss on the whole.
Solution :
Investment = ₹ 131040
N.V. of 1 share = ₹ 100
Discoount = 9% of ₹ 100 = ₹ 9
∴ MV. of 1 share = ₹ 100 - ₹ 9 = ₹ 91
∴ Number of shares purchased = (Investment/M.V of 1 share) = 131040/91 = 1440
Number of shares worth ₹ 72000 = 72000/100 = 720
∴ Mrs. Kulkarni sells 720 shares at a premium of 10%
M.V. of 1 share = ₹ 100 + ₹ 10 = ₹ 110
∴ Selling price of 720 shares = 720 x ₹ 110 = 79200
Number of remaining shares = 1440 - 720 = 720
She sells 720 shares at a discount of 5%
M.V. of 1 share = ₹ 100 - ₹ 5 = ₹ 95
∴ Selling price of 720 shares = 720 x ₹ 95 = ₹ 68400
∴ Total selling price = ₹ (79200 + 68400) = ₹ 147600
∴ Total gain = Total selling price - Total investment
= 147600 - 131040
= ₹ 16560
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3.
A man invests a certain sum on buying 15% ₹ 100 shares at 20% premium. Find :
(i) His income from one share
(ii) The number of shares bought to have an income, from the dividend, ₹ 6480
(iii) Sum invested
Solution :
(i) Divident on one share = 15% of ₹ 100
= ₹ (15/100 x 100)
= ₹ 15
so, the income from one share is ₹ 15
(ii) Number of shares bought by the man
= annual income / divident on one share
= 6480/15
= ₹ 432
(iii) Since the man bought shares of ₹ 100 at 20% premium, the market value of one share
= ₹ (1 + 20/100) x 100
= ₹ (120/100) x 100
= ₹ 120
∴ His total investment = numer of shares x market value of one share
= 432 x 120
= ₹ 51,840
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4.
Gagan invested ₹ 80% of his savings in 10% ₹ 100 shares at 20% premium and the rest of his savings in 20% ₹ 50 shares at ₹ 20% discount. If his incomes from these shares is ₹ 5,600 calculate:
(i) His investment in shares on the whole
(ii) The number of shares of first kind that he bought
(iii) Percentage return, on the shares bought on the whole.
Solution :
(i) Let the total savings be ₹ x
For 1st part:
N.V. of each share = ₹ 100
M.V. of each share = 100 + 20/100 (100) = ₹ 120
Number of shares bought = 0.8/120 .............. (Investment = ₹ x)
Dividend on each share = 10% of 100 = ₹ 10 ..........(Rate = 10%)
Total dividend = 10 x 0.8x/120 = ₹ 0.8x/12
For 2nd part:
N.V. of each share = ₹ 50
M.V. of each share = 50-20/100 (50) = ₹ 40
Number of shares bought = 0.2x/40 .............(Investment = ₹ x)
Dividend on each share = 20% of 50 = ₹ 10 ............(Rate = 20%)
Total dividend = 10 x 0.2x/40 = 0.2x/4
Given that dividends(incomes) from both the investments are is ₹ 5600
⇒ 0.8/12 + 0.2x/4 = 5600
⇒ (0.8x + 0.6x)/12 =5600
⇒ x = 5600 x 12/1.4
⇒ x = 48000
Thus, his investment in shares on the whole is ₹ 48000
(ii) So, number of shares bought = 0.8x/120 = (0.8 x 48000)/120 = ₹ 320
(iii) The total dividend (return) = 0.8x/12 + 0.2x/4
= (0.8 x 48000)/12 + (0.2 x 48000)/4
= 0.8 x 4000 + 0.2 x 12000
= ₹ 5600
Percentage return = 5600/48000 x 100 = 11 2/3%
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5.
Ashwarya bought 496, ₹ 100 shares at ₹ 132 each, find :
(i) Investment made by her
(ii) Income of Ashwarya from these shares, if the rate of dividend is 7.5%.
(iii) How much extra must ashwarya invest in order to increase her income by ₹ 7,200.
Solution :
(i) N.V. of each share = ₹ 100
M.V. of each share = ₹ 132
Investment made by her = 496 x 132 = ₹ 65,472
(ii) dividend on 1 share = 7.5% of ₹ 100 = ₹ 7.5
so, income of Ashwarya from these shares = 496 x 7.5 = ₹ 3,720
(iii) If she wants to increase her income by ₹ 7,200
the number of shares she should buy = (increase in the income / income of one share)
= 7200/7.5 = ₹ 960
So, she should invest = 960 x 7.5 = ₹ 1,26,720
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6.
A company pays a dividend of 15% on its ₹ 100 shares from which income tax at the rate of 20% is deducted. Find :
(i) The net annual income of Gopal who owns 7,200 shares of this company
(ii) The sum invested by Ramesh when the shares of this company are bought by him at 20% premium and the gain required by him(after deduction of income tax) is ₹ 9,000
Solution :
(i) Let the number of shares be X.
Annual income = Rate of dividend x Nominal value x Number of shares
= (15/100) x 100 x X
= 15x ________________(i)
Since the income tax is geven to be 20% which is deducted,
15x - 20% of 15x = 15x - 20/100 (15x) = 15x - 3x = 12x
Thus, the net annual income of Gopal who owns 7,200 shares of the company
= 12x
= 12 x 7200
= ₹ 86,400
(ii) Let the sum invested by him be ₹ S
N.V. of each share = ₹ 100
M.V. of each share = ₹ 100 + 20% of ₹ 100 = ₹ 120
Number of each share = ₹ S/120
Dividend on each share = ₹ 15% of ₹ 100 = ₹ 15
Total dividend = ₹ 15 x s/120 = ₹ S/8
Since the income tax is given to be 20% which is deducted,
The gain = S/8 - 20/100 x S/8 = S/8 - S/40 = S/10
Given the gain required by him is ₹ 9000
So, S/10 = 9000
⇒ S = ₹ 90,000
Hence, the sum invested by Ramesh is ₹ 90,000
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7. Mr. Joseph sold some ₹ 100 shares paying 10% dividend at a discount of 25% and invested the proceeds in ₹ 100 shares paying 16% dividend at a discount of 20%. By doing so, his income was increased by ₹ 4,800. Find the number of shares originally held by Mr. Joseph.
Solution :
Let he number of shares be X.
Annual income = Rate of dividend x Nominal Value x Number of shares
= 10/100 x 100 x X
= 10X _____________________(i)
Since each share is sold at a discount of 25%
selling price of one share = ₹ 100 - 25/100 = ₹ 75
So, selling price of X share = ₹ 75X
The proceeds = the new investment = ₹ 75X
Here the N.V. = ₹ 100
M.V. of each share = ₹ 80
Rate of dividend = 16%
Number of shares = 75X/80
Annual income = Rate of dividend x Nominal Value x Number of shares
= 10/100 x 100 x 75X/80
= 15X ___________________(ii)
From (i) and (ii), we get
15X - 10X = 4800
⇒ 5X = 4800
⇒ X = 960
So, the muber of shares originally were 960.
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8. Gopal has some ₹ 100 shares of company A, paying 10% dividend. He sells a certain number of these shares at a discount of 20% and invests the proceeds in ₹ 100 shares at ₹ 60 of company B paying 20% dividend. If his income, from the shares sold, increases by ₹ 18,000, find the number of shares sold by Gopal.
Solution :
Let the number of shares the man sold be X.
N.V. of share = ₹ 100
Rate of dividend = 10%
Dividend on each share = 10% of ₹ 100 = ₹ 10
So, the dividend on X shares = ₹ 10 x X = ₹ 10X
Selling price of each share = ₹ 100 - 20% of ₹ 100 = ₹ 80
Amount obtained on selling X shares = ₹ 80 x X = ₹ 80X
The proceeds he invested in ₹ 100 shares at ₹ 60 of company B
paying 20% dividend.
N.V. of share = ₹ 100
M.V. of each share = ₹ 60
Number of shares bought by the man = Amount invested/M.V. of each share
= 80X / 60
= 4X / 3
Dividend on each share = 20% of ₹ 100 = ₹ 20
Total dividend reeived = Dividend on each share x Number of shares
= 20 x 4X/3
= 80X/3
Increase in the income = ₹ 18000
⇒ 80X/3 - 10X = 18000
⇒ 50X/3 = 18000
X = ₹ 1080
Hence, the number of shares sold by Gopal is ₹ 1080
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9. A man invests a certain sum of money in 6% hundred-rupee shares at ₹ 12 premium. When the shares fell to ₹ 96, he sold out all the shares bought and invested the proceed in 10%, ten-rupee shares at ₹ 8. If the change in his income is ₹ 540, Find the sum invested originally
Solution :
Let the original sum invested = X
Then number of ₹ 100 shares purchased at premium of ₹ 12
= X/(100 + 12) = X/112
The income per original share at 6% = ₹ 6
Total income = (Number of shares) x (earning per share)
= (Number of shares) x 6 = X/112 x 6 = 3X/56
Proceeds from sale of original shares at ₹ 96 per share
= (Number of shares) x 96 = X/112 x 96 = 6X/7
Number of ₹ 10 shares purchased at ₹ 8 per share from proceeds of original shares
= (Proceeds from sale of iriginal shares)/8 = (6X/7)/8 = 3X/28
Income per new share of ₹ 10 at 10% = 10/100 x 10 = ₹ 1
Total income from new shares
= (Number of shares) x (Income per share)
= (3X/28) x 1 = 3X/28
Given change in income = 540
Income from old shares - Income from new shares = 540
∴ 540 = 3X/28 - 3X/56
∴ 540 = 3X/56
∴ X = (540 x 56)/3 = 10,080
Thus, the original sum invested is ₹ 10,080.
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10.
Mr. Gupta has a choice to invest in ten-rupee shares of two firms at ₹ 13 or at ₹ 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 Mr. Gupta invests equally in both the firms and the difference between the returns from them is ₹ 30, find how much, in all, does he invest.
Solution :
(i) 1st firm
Nominal value of 1 share = ₹ 10
Market value of 1 share = ₹ 13
Dividend% = 5%
Dividend = 5% of ₹ 10 = ₹ 0.50
∴ Income% = (Income/Investment) x 100%
= 0.50/13 x 100%
= 3.846%
2nd firm
Nominal value of 1 share = ₹ 10
Market value of 1 share = ₹ 16
Dividend% = 6%
Dividend = 6% of ₹ 10 = ₹ 0.60
∴ Income% = (Income/Investment) x 100%
= 0.60/16 x 100%
= 3.75%
Then first firm is paying better than second firm.
(ii) Let money invested in each firm = ₹ y
For 1st firm
∴ No. of shares purchased = y/13 shares
Total dividend = ₹ 0.50 x y/13 = ₹ y/26
for 2nd firm
∴ No. of shares purchased = y/16 shares
Total dividend = ₹ 0.60 x y/16 = ₹ 3y/80
Given difference of both dividend = ₹ 30
⇒ y/26 - 3y/80 = ₹ 30
⇒ y/1040 = ₹ 30
⇒ y = ₹ 30 x 1040 = ₹ 31,200
Total money invested in both firms = ₹ 31,200 × 2
= ₹ 62,400
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11.
Ashok invested ₹ 26,400 in 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 :
(i) Total dividend = ₹ 2,475
And, dividend on each share = 12% of ₹ 25 = 12/100 x ₹ 25 = ₹ 3
∴ Number of shares bought = (Total dividend / Dvidend on 1 share) = 2475/3 = 825
(ii) Market value of 825 shares = ₹ 26,400
∴ Market value of each share = (Total investement / No. of shares) = 26400/825 = ₹ 32
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12.
A man invested ₹ 45,000 in 15% Rs100shares quoted at ₹ 125. When the market value of these shares rose to ₹ 140, he sold some shares, just enough to raise ₹ 8,400. Calculate:
(i) the number of shares he still holds;
(ii) the dividend due to him on these remaining shares.
Solution :
(i) Total investment = ₹ 45,000
Market value of 1 share = ₹ 125
∴ No of shares purchased = 45/ 125 } = 360 shares
Nominal value of 360 shares = ₹ 100 × 360= ₹ 36,000
Let no. of shares sold = n
Then sale price of 1 share = ₹ 140
Total sale price of n shares = ₹ 8,400
Then n = 8/ 140 } = 60 shares
The no. of shares he still holds = 360 – 60 = 300
(ii) Nominal value of 300 shares = ₹ 100 × 300 = ₹ 30,000
Dividend% = 15%
Dividend = 15% of ₹ 30,000
= 15/100 × 30,000 = ₹ 4,500
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13.
Mr.Tiwari. invested ₹ 29,040 in 15% Rs100 shares quoted at a premium of 20%. Calculate:
(i) the number of shares bought by Mr. Tiwari.
(ii) Mr. Tiwari’s income from the investment.
(iii) the percentage return on his investment.
Solution :
Total investment = ₹ 29,040
Nominal value of 1 share = ₹ 100
Market value of 1 share = ₹ 100+ 20% of ₹ 100
= ₹ 100 + ₹ 20 = ₹ 120
∴ No of shares purchased = 29/ 120 } = 242 shares
Nominal value of 242 shares = ₹ 100 x 242 = ₹ 24,200
Dividend% = 15%
Dividend = 15% of ₹ 24,200
= 15/100 × 24,200 = ₹ 3,630
Income % = (Income/Investment) x 100%
= (3630/29040) x 100%
= 12.5 %
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14.
A dividend of 12% was declared on ₹ 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 ₹ 1,350.
Solution :
(i) Nominal value of 1 share = ₹ 150
Dividend % = 12%
Dividend on 1 share = 12% of ₹ 150
= 12/100 x ₹ 150 = ₹ 18
Let market value of 1 share = ₹ y
Return % = 10%
10% of ₹ y = ₹ 18
⇒ 10/100 x y = ₹ 18
⇒ y = ₹ 180
(ii) When dividend is ₹ 18, then investment is ₹ 180
When dividend is ₹ 1,350, then investment
= 180/18 x ₹ 1350
= ₹ 13,500
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15. Divide ₹ 50,760 into two parts such that if one part is invested in 8% ₹ 100 shares at 8% discount and the other in 9% ₹ 100 shares at 8% premium, the annual incomes from both the investments are equal.
Solution :
Total investment = ₹ 50,760
Let 1st part = ₹ y
2nd part = ₹ (50760 - y)
For 1st part
Nominal value of 1 share = ₹ 100
Market value of 1 share = ₹ 100 - 8% of ₹ 100
= ₹ 100 - ₹ 8 = ₹ 92
∴ No. of shares purchased = y/92 shares
Dividend % = 8%
Dividend on 1 share = 8% of ₹ 100 = ₹ 8
Total dividend = y/92 x ₹ 8 = ₹ 2y/23
For 2nd part
Nominal value of 1 share = ₹ 100
Market value of 1 share = ₹ 100 + 8% of ₹ 100
= ₹ 100 + ₹ 8 = ₹ 108
∴ No. of shares purchased = (50760-y)/108 shares
Dividend % =9%
Dividend on 1 share = 9% of ₹ 100 = ₹ 9
Total dividend = (50760-y)/108 x ₹ 9 = 9 x (50760-y)/108
Given that both dividend are equal
Then ₹ 2y/23 = 9 x (50760-y)/108
⇒ 2y x 108 = 23 (456840 - 9y)
⇒ 216y = 23 x 456840 - 207y
⇒ 216y + 207y = 23 x 456840
⇒ 423y = 23 x 456840
⇒ 423y = 23 x 456840
⇒ y = (23 x 456840)/423
⇒ y = ₹ 24,840
1st part = ₹ 24,840
2nd part = ₹ 50,760 - ₹ 24,840 = ₹ 25,920
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16.
Mr. Shameem invested 33 1/3% of his savings in 20% ₹ 50 shares quoted at ₹ 60 and the remainder of the savings in 10% ₹ 100 share quoted at ₹ 110. If his total income from these investments is ₹ 9,200; find :
(i) his total savings
(ii) the number of ₹ 50 share
(iii) the number of ₹ 100 share.
Solution :
Let his total savings is ₹ y
1st case
His saving = 33 1/3% of y = ₹ y/3
margket price of 1 share = ₹ 60
Then shares purchased = y/(3 x 60) = y/180
Dividend on 1 share = 20% of ₹ 50 = ₹ 10
Total dividend = y/180 x 10 = ₹ y/18
2nd case
His savinf = 66 2/3% of y = ₹ 2y/3
Market price of 1 share = ₹ 110
Then shares purchased = 2y/(3 x 110) = y/165
Dividend on 1 share = 10 % of ₹ 100 = ₹ 10
Total dividend = y/165 x 10 = ₹ 2y/33
According to question
Total income = ₹ 9200
⇒ y/18 + 2y/33 = ₹ 9200
⇒ 23y/198 = ₹ 9200
⇒ 23y = 9200 x 198
⇒ y = (9200 x 198)/23 = ₹ 79200 Ans.
The number of ₹ 50 share = 79200/180 = 440 Ans.
The number of ₹ 100 share = 79200/165 = 480 Ans.
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17.
Vivek invests ₹ 4,500 in 8%, ₹ 10 shares at ₹ 5. 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 :
1st case
Total investment = ₹ 4,500
Market value of 1 share = ₹ 15
∴ No of shares purchased = 4/ 15 } = 300 shares
Nominal value of 1 share = ₹ 10
Nominal value of 300 shares = ₹ 10 × 300= ₹ 3,000
Dividend = 8% of ₹ 3,000
= 8/100 × 3,000 = ₹ 240
Sale price of 1 share = ₹ 30
Total sale price= ₹ 30 × 300= ₹ 9,000
(ii) new market price of 1 share= ₹ 125
∴ No of shares purchased = 9/ 125 } = 72 shares
(iii) New nominal value of 1 share= ₹ 100
New nominal value of 72 shares = ₹ 100 × 72 = ₹ 7,200
Dividend% = 12%
New dividend = 12% of ₹ 7,200
= 12/100 × 7,200 = ₹ 864
Change in annual income = ₹ 864 – ₹ 240 = ₹ 624
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18.
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 :
Rate of dividend = 8%
Investment = ₹ 52000
Market Rate = ₹ 100 – 20 = ₹ 80
No. of shares purchased = 52000/80 = 650
(i) Annual dividend = 650 × 8 = ₹ 5200
(ii) On selling, market rate = ₹ 100+20 = ₹ 120
⇒ Sale price = 650 × 120 = ₹ 78000
Profit = ₹ 78000 – ₹ 52000 = ₹ 26000
⇒ Total gain = 26000 + 5200 = ₹ 31200
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19.
Salman buys 50 shares of face value ₹ 100 available at ₹ 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 ₹ 150, how many extra shares should he buy?
Solution :
Number of shares bought = 50
N.V. of one share = ₹ 100
M.V. of each share = ₹ 132
(i) Investment = M.V. of each share x Number of shares
= ₹ 132 x 50
= ₹ 6600
(ii) Since dividend on 1 share = 7.5% of N.V. = 7.5/100 x 100 = ₹ 7.50
His annual icome = ₹ 7.50 x 50 = ₹ 375
(iii) Extra shares to be bought = Increase in annual income income in one share = 150/7.50 = 20
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20.
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 :
N.V. of each share = ₹ 50
M.V. of each share = ₹ 50 + 20% of ₹ 50
= 50 + (20/100) x 50
= 50 + 10
= ₹ 60
Dividendt on one share = 15% of ₹ 50 = (15/100) x 50 = 7.5
(i) Number os shares bought = (Total dividend / Dividend on one share) = 600/7.5 = 80
(ii) His total investment = Number of shares x M.V. of one share
= 80 x ₹ 60
= ₹ 4800
(iii) Rate of return = (Total dividend / Total investment) x 100%
= 600/4800 x 100% = 12.5%
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21.
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 market value = 100 +20 = ₹ 120
Money required to buy 1 share = ₹ 120
∴ Number of shares = (Money Invested / Market Value of 1 share)
= 9600/120 = 80
(ii) Each share is sold at ₹ 160
∴ Sale Proceeds = 80 x ₹ 160 = ₹ 12,800
(iii) Now, investment = ₹ 12800
Dividend = 10%
Net Value = 50
Market Value = ₹ 40
∴ Number of shares = (Investment / Market Value)
= 12800/40 = 320
(iv) Now, dividend on 1 share = 10% of N.V. = 10% of 50 = 5
⇒ Dividend on 320 shares = 320 x 5 = 1600
Thus, change in two dividends = 1600 - 640 = 960
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22. How much should a man invest in ₹ 50 shares selling at ₹ 60 to obtain an income of ₹ 450, if the rate of dividend declared is 10%. Also find his yield percent, to the nearest whole number.
Solution :
Face value of each share = ₹ 50
Dividend % = 10%
Dividend on 1 share = 10/100 x 50 = ₹ 5
∴ Number of shares bought = (Total dividend / Dividend per share) = 450/5 = 90
Market value of each share = ₹ 60
∴ Total investment = 90 x 60 = ₹ 5400
Percentage return = (Total dividend / Total investment) x 100
= (450/5400) x 100
= 8.33 %
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