# ICSE Solutions for Chapter 3 Shares and Dividend Class 10 Mathematics

Question 1: By investing  ₹ 45,000 in 10% ₹ 100 shares, Sharad gets ₹ 3,000 as dividend. Find the market value of each share.

Solution 1: Annual income from 1 share = 10% of Rs.100 = Rs 10
Total annual income = Rs 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 = Rs 150

Question 2. Mrs. Kulkarni invests ₹ 1,31,040 in buying ₹ 100 shares at a discount of 9%. She sells shares worth Rs 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 2: Investment = Rs 1,31,040
NV. of 1 share  = Rs 100
Discount  = 9% of Rs 100 = Rs 9
∴ MV. of 1 share  = Rs 100 - Rs 9 =  Rs 91
∴ Number of shares purchased = (Investment/M.V. of 1 share) = 131040/91 = 1440
Number of shares worth Rs 72000 =  72000/100 = 720
∴ Mrs. Kulkarni sells 720 shares at a premium of 10%
M.V. of 1 share = Rs 100 + Rs 10 =  Rs 110
∴ Selling price of 720 shares = 720 × Rs 110 = Rs 79200
Number of remaining shares = 1440 - 720 = 720
She sells 720 shares at a discount of 5%
M.V. of 1 share = Rs 100 – Rs 5 = Rs 95
∴ Selling price of 720 shares = 720 × Rs 95 = Rs. 68400
∴ Total selling price = Rs. (79200 + 68400) = Rs 1,47,600
∴ Total gain  = Total selling price - Total investment
= Rs (147600 - 131040)
= Rs 16,560

Question 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 3: (i) Dividend on one share =  15% of Rs 100
= Rs (15/100 × 100)
= Rs 15
So, the income from one share is Rs 15

(ii) Number of shares bought by the man
= (annual income/dividend on one share)
=  (6480/15)
= Rs 432

(iii) Since the man bought shares of Rs 100 at 20% premium, the market value of one share
= Rs (1 + 200/100)  × 100
= Rs (120/100 × 100)
= Rs 120
∴ His total investment = (number of shares × market value of one share)
= 432 × 120
= Rs 51,840

Question 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 4: (i) Let the total savings be Rs x
For 1st part:
N.V. of each share = Rs 100
M.V. of each share = 100 + {(20/100) ×100} =  Rs 120
Number of shares bought = 0.8x/120 ...(Investment = Rs x)
Dividend on each share = 10% of 100 =  Rs. 10 ...(Rate =  10%)
Total dividend = 10 × (0.8x/120) = Rs 0.8x/12
For 2nd part:
N.V. of each share = Rs 50
M.V. of each share = 50 – {20/100(50)}  = Rs 40
Number of shares bought  = 0.2x/40 ...(Investment = Rs  x)
Dividend on each share = 20% of 50 = Rs 10 ...(Rate = 20%)
Total dividend = 10 × (0.2x/40) = 0.2x/4
Given that dividends (incomes) from both the investments are is Rs 5,600.
⇒ 0.8x/12 + 0.2x/4 = 5600
⇒ {(0.8x + 0.6x)/12} = 5600
⇒ x = {(5600 × 12)/1.4}
⇒ x = 48,000
Thus, his investment in shares on the whole is Rs 48,000

(ii) So, number of shares bought = 0.8x/120 = {(0.8 × 48,00)/120} = Rs 320

(iii) The total dividend(return) = (0.8x/12 + 0.2x/4)
= {0.8(48,000)/12} = {0.2(48,000)/4}
= 0.8 × 4,000 + 0.2 ×12,000
= Rs 5600
Percentage return = (5600/48,000 × 100) = 11.2/3%

Question 5. 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 m)
(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 5: (i) Let the number of shares be x.
Annual income = Rate of dividend x Nominal Value x Number of shares
= 15/100 × 100× x
= 15x ...(i)
Since the income tax is given 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 this company
= 12x
= 12×(7,200)
= Rs. 86,400

(ii) Let the sum invested by him be Rs S
N.V. of each share = Rs 100
M.V. of each share = Rs 100 + 20% of Rs 100 =  Rs 120
Number of each share = Rs S/120
Dividend on each share = Rs 15% of Rs 100 = Rs 15
Total dividend = Rs {15 × S/120} = Rs S/8
Since the income tax is given to be 20% which is deducted,
The gain = S/8 –{20/100 (S/8)} = (S/8 -  S/40) = S/10
Given the gain required by him is Rs 9000.
So, S/10 = 9000
⇒ S = Rs 90,000
Hence, the sum invested by Ramesh is Rs 90,000.

Question 6. 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 6: Let the number of shares be x.
Annual income = (Rate of dividend × Nominal Value x Number of shares)
= (10/100 × 100 × x)
= 10x      ......(i)
Since each share is sold at a discount of 25%,
selling price of one share = Rs (100 – 25/100)  = Rs 75
So, selling price of x shares =  Rs 75x
The proceeds =  the new investment = Rs 75x
Here the N.V. = Rs 100
M.V. of each share = Rs 80
Rate of dividend = 16%
Number of shares = 75x/80
Annual income = Rate of dividend x Nominal Value x Number of shares
=  16/100 × 100 × 75x/80
From (i) and (ii), we get
15x - 10x = 4800
⇒ 5x = 4800
⇒ x = 960
So, the number of shares originally were 960.

Question 7: Ashwarya bought 496, ₹ 100 shares at ₹ 132 each, find:
(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 7:
(i) N.V. of each share =  Rs 100
M.V. of each share = Rs 132
Investment made by her = 496 × 132 = Rs 65, 472

(ii) Dividend on 1 share = 7.5% of Rs 100 = Rs 7.5
So, income of Ashwarya from these shares = 496 × 7.5 = Rs 3,720
(iii) If she wants to increase her income by Rs 7,200
the number of shares she should buy = (increase in the income/income of one share) = 7,200/7.5 = Rs 960
So, she should invest = 960 × 7.5 = Rs 1,26,720

Question 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 8: Let the number of shares the man sold be x.
N.V. of share = Rs 100
Rate of dividend = 10%
Dividend on each share = 10% of Rs 100 = Rs 10
So, the dividend on x shares = Rs 10 × x = Rs 10x
Selling price of each share = Rs 100 - 20% of Rs 100 = Rs 80
Amount obtained on selling x shares =  Rs 80 × x = Rs 80x
The proceeds he invested in Rs 100 shares at Rs. 60 of company B paying 20% dividend.
N.V. of share = Rs 100
M.V. of each share = Rs 60 = Rs 60
Number of shares bought by the man = (Amount invested/M.V. of each share)
Dividend on each share = 20% of Rs 100 = Rs 20
Total dividend received = Dividend on each share × Number of shares
= 20 × 4x/3
= 80x/3
Increase in the income = Rs 18,000
⇒ 80x/3 – 10x = 18,000
⇒ 50x/3  = 18,000
x = Rs 1080
Hence, the number of shares sold by Gopal is Rs 1080.

Question 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 9: Let the riginal sum invested  = x
Then number of Rs 100 shares purchased at premium of Rs 12
= x/(100 + 12) =  x/112
The income per original share at 6% = Rs 6
Total Income = (Number of shares) × (earning per share)
= (Number of shares) × 6 = x/112 × 6  = 3x/56
Proceeds from sale of original shares at Rs. 96 per share
= (Number of Shares) × 96  = x/112 × 96 = 6x/7
Number of Rs. 10 shares purchased at Rs 8 per share from proceeds of original shares
= {(Proceeds from sale of original shares)/8} = {(6x/7)/8} = 3x/28
Income per new share of Rs 10 at 10% = (10/100 ×10)  = Rs 1
Total income from new shares
= (Number of shares) × (Income per share)
= 3x/28 × 1 = 3x/28
Given change in income = 540
Income from old shares - Income from new shares = 540
∴  540 = 3x/28 – 3x/56 = 3x/56
∴  x = {(540/3)/56} = 10,080
Thus, the original sum invested is Rs 10,080.

Question 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 10:
(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) × 100%
= (0.50/13) × 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) ×100 %
= (0.60/16 × 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/13shares
Total dividend = Rs 0.50 × y/13 = Rs y/26
For 2nd firm
∴ No. of shares purchased = y/16shares
Total dividend = Rs 0.60 × y/16 = Rs 3y/80
Given difference of both dividend = Rs 30
⇒ y/26 – 3y/80 = Rs 30
⇒ y/1040 = Rs 30
⇒ y = Rs 30 × 1040 =  31,200
Total money invested in both firms = ₹ 31,200 × 2
= ₹ 62,400