Question

Rao sold a certain number of Rs. 20 shares paying 8% dividend at Rs. 18
and invested the proceeds in Rs. 10 shares, paying 12% dividend at 50%
premium. If the change in his annual income is Rs. 120, find the number of
shares sold by Rao.*​

Answer 1

Given :

Rao sold some shares paying dividend and bought new shares which pays some dividend the difference in income it Rs. 120.

Solution:

Let the number of shares Rao sold = x

Income on one share = 8% of 20

                                   = 0.08 × 20

                                   = ₹ 1.60

Total income from shares = 1.60x

Since x shares sold at Rupees 18, the value of sold shares = 18x

Selling amount is invested in Rs. 10 shares at 50% of premium.

Market value of the new shares = $10+\frac{50}{100}$

                                                     = ₹ 15.00

Total number of shares purchased = $\frac{\text{total amount invested}}{\text{MV of one share}}$

                                                         $=\frac{18x}{15}$

Dividend received for one share = 12% of 10

                                                      = 1.20

As per given statement in the question "the change in his annual income is Rs. 120."

considering the change is increase of Rs. 120 in income, So the new income would be

$\frac{1.6x+120}{1.20}=\frac{18x}{15}$

(1.6x + 120) × 15 = 18x × 1.20

24x + 1800 = 21.6x

2.4x + 1800 = 0

x = -750

Number of shares can not be in negative so now we consider the difference in his income of Rs. 120 is decreasing.

$\frac{1.6x-120}{1.20}=\frac{18x}{15}$

(1.6x -120) × 15 = 18x × 1.20

24x - 1800 = 21.6x

24x - 1800 = 0

x = 1800/24

x = 750

750 shares sold by Rao.