# 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

= (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

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

Dividend on each share = 10% of 100 = Rs. 10

Total dividend = 10 × (0.8x/120) = Rs 0.8x/12

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

Dividend on each share = 20% of 50 = Rs 10

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

= 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%

Annual income = Rate of dividend x Nominal Value x Number of shares

= 15/100 × 100× x

= 15x

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)

= {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.

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.

(i) N.V. of each share = Rs 100

M.V. of each share = Rs 132

Investment made by her = 496 × 132 = Rs 65, 472

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:****(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 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

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.

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

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 = xThen 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.

(i)

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%

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.

= (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 = ₹ 10Market 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

Total dividend = Rs 0.50 × y/13 = Rs y/26

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

__For 1st firm__

∴ No. of shares purchased = y/13sharesTotal dividend = Rs 0.50 × y/13 = Rs y/26

__For 2nd firm__

∴ No. of shares purchased = y/16sharesTotal 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