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.

Let the number of shares Gopal sold be x.

N.V. = ₹ 100

Rate of dividend = 10%

Dividend = No. of shares × Rate of div. × N.V. of 1 share

= x $\times \dfrac{10}{100} \times 100$

= 10x.

S.P. = ₹ 100 - 20% of ₹ 100

= ₹ 100 - $\dfrac{20}{100} \times 100$

= ₹ 100 - ₹ 20

= ₹ 80.

Amount obtained on selling x shares = ₹ 80x.

The proceeds he invested in ₹ 100 shares at ₹ 60 of company B paying 20% dividend.

N.V. = ₹ 100

M.V. = ₹ 60

No. of shares bought by man = $\dfrac{\text{Amount invested}}{\text{M.V.}} = \dfrac{80x}{60} = \dfrac{4x}{3}.$

Dividend = No. of shares × Rate of div. × N.V. of 1 share

= $\dfrac{4x}{3} \times \dfrac{20}{100} \times 100$

= $\dfrac{80x}{3}$.

Given, increase in income = ₹ 18000

$\therefore \dfrac{80x}{3} - 10x = 18000 \\[1em] \Rightarrow \dfrac{80x - 30x}{3} = 18000 \\[1em] \Rightarrow \dfrac{50x}{3} = 18000 \\[1em] \Rightarrow x = \dfrac{18000 \times 3}{50} \\[1em] \Rightarrow x = 1080.$

Hence, no.of shares sold by Gopal is 1080.