Vimal sold a certain number of ₹ 20 shares paying 8% dividend at ₹ 18 and invested the proceeds in ₹ 10 shares paying 12% dividend at 50% premium (i.e. ₹ 15). If his annual income decreases by ₹ 120, find the number of shares sold by Vimal.

Let the number of shares Vimal sold be x.

For initial shares,

N.V. = ₹ 20

Rate of dividend = 8%

By formula,

Annual income (from first investment) = No. of shares × Rate of div. × N.V. of 1 share

$= x \times \dfrac{8}{100} \times 20 = \dfrac{8x}{5}$

S.P. of each share = ₹ 18.

Amount obtained on selling shares = S.P × No. of shares = ₹ 18x.

The proceeds he invested in ₹ 10 shares at ₹ 15, paying 12% dividend.

N.V. = ₹ 10

M.V. = ₹ 15

No. of shares bought by man = $\dfrac{\text{Amount invested}}{\text{M.V. of each share}} = \dfrac{18x}{15} = \dfrac{6x}{5}.$

By formula,

Annual income (from second investment) = No. of shares × Rate of div. × N.V. of 1 share

$= \dfrac{6x}{5} \times \dfrac{12}{100} \times 10$

$= \dfrac{720x}{500} = \dfrac{36x}{25}$.

Given, decrease in income = ₹ 120

$\therefore \dfrac{8x}{5} - \dfrac{36x}{25} = 120 \\[1em] \Rightarrow \dfrac{40x - 36x}{25} = 120 \\[1em] \Rightarrow \dfrac{4x}{25} = 120 \\[1em] \Rightarrow x = \dfrac{120 \times 25}{4} \\[1em] \Rightarrow x = 750.$

Hence, Vimal sold 750 shares.