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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.
Solution
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.
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