A man sold some ₹ 20 shares, paying 8% dividend, at 10% discount and invested the proceeds in ₹ 10 shares, paying 12% dividend, at 50% premium. If the change in his annual income is ₹ 600, find the number of shares sold by the man.

N.V. of share = ₹ 20

M.V. of share = N.V. - Discount

= ₹ 20 - 10% of 20

= ₹ 20 - $\dfrac{10}{100} \times 20$

= ₹ 20 - ₹ 2 = ₹ 18.

∴ Dividend on 1 share = 8% of ₹ 20 = $\dfrac{8}{100} \times 20$ = ₹ 1.60

Let no. of shares purchased be x.

Dividend on x number of shares = 1.6x

S.P. of each share = ₹ 18

S.P. of x shares (Sum invested) = ₹ 18x

In 2nd investment

N.V. of share = ₹ 10

M.V. of share = N.V. + Premium

= ₹ 10 + 50% of 10

= ₹ 10 + ₹ 5

= ₹ 15

No. of shares purchased = $\dfrac{\text{Investment}}{\text{M.V. of share}} = \dfrac{18x}{15}$

∴ Dividend on 1 share = 12% of ₹ 10 = $\dfrac{12}{100} \times 10$ = ₹ 1.2.

Total income = 1.2 × $\dfrac{18x}{15} = \dfrac{21.6x}{15}$ = 1.44x

Given,

Change in income = ₹ 600

⇒ 1.6x - 1.44x = 600

⇒ 0.16x = 600

⇒ x = $\dfrac{600}{0.16}$ = 3750.

Hence, no. of shares sold = 3750.