A man sold some ₹100 shares paying 10% dividend at a discount of 25% and invested the proceeds in ₹100 shares paying 16% dividend quoted at ₹80 and thus increased his income by ₹2000. Find the number of shares sold by him.

Let the number of shares sold by the man be x

The man sold the shares at a discount of 25%,
∴ Selling price of the shares = ₹100 - 25% of ₹100 = ₹100 - ₹25 = ₹75

Sales proceeds = ₹75x

Number of ₹100 16% shares purchased by the man

$= \dfrac{75x}{80} \\[0.5em] = \dfrac{15x}{16}$

Annual Income from previous shares = No. of shares x Rate of Dividend x Nominal Value per share

$= x \times \dfrac{10}{100} \times 100 \\[0.5em] = \bold{₹10x}$

Annual Income from new shares = No. of shares x Rate of Dividend x Nominal Value per share

$= \dfrac{15x}{16} \times \dfrac{16}{100} \times 100 \\[0.5em] = \bold{₹15x}$

As per the given,

$15x - 10x = 2000 \ 5x = 2000 \ x = 400$

∴ Number of shares sold by the man = 400