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 share 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 invest 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

Number of shares bought by the man = `"Amount invested"/"M.V of each share"`

= `(80x)/60`

= `(4x)/3`

Dividend on each share = 20% of Rs. 100 = Rs. 20

Total dividend recieved = Dividend on each share × Number of shares 

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

= `(80x)/3`

Increase in the income = Rs. 18,000

⇒ `(80x)/3 - 10x = 18000`

⇒ `(50x)/3 = 18000`

x = Rs. 1080

Hence, the number of shares sold by Gopal is Rs. 1080.