Question

Gopal has some Rs. 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 Rs. 100 shares at Rs. 60 of company B paying 20% dividend. If his income, from the shares, sold, increases by Rs. 18,000, find the number of shares sold by Gopal. 

Answer 1

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 xx 10/100 xx 100`

= 10x

S.P. = ₹ 100 − 20% of ₹ 100

= ₹ 100 − `20/100 xx 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 = `("Amount invested")/("M. V.") = (80x)/60 = (4x)/3`

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

= `(4x)/3 xx 20/100 xx 100`

= `(80x)/3`

Given, increase in income = ₹ 18000

∴ `(80x)/3 - 10x = 18000`

⇒ `(80x - 30x)/3 = 18000`

⇒ `(50x)/3 = 18000`

⇒ x = `(18000 xx 3)/50`

⇒ x = 1080

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