Question

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. If his annual dividend income decreases by ₹ 120, find the number of shares sold by Vimal.

Answer 1

Given:

Let x = Number of ₹ 20 shares Vimal sold.

Face value of old shares = ₹ 20, Dividend = 8%.

He sold them at ₹ 18 each and invested proceeds in ₹ 10 shares with 12% dividend, bought at 50% premium (market price = ₹ 15).

His annual dividend income decreases by ₹ 120.

Step-wise calculation:

1. Annual income from old shares

= x × 8% of ₹ 20 

= `x xx 8/100 xx 20` 

= `x xx 8/5` 

= 1.6x

2. Sale proceeds

= x × ₹ 18 

= 18x

3. Market price of new ₹ 10 share at 50% premium

= `10 xx (1 + 50/100)`

= ₹ 15

4. Number of new shares bought

= `(18x)/15` 

= `(6x)/5`

5. Annual income from new shares

= `(6x)/5 xx 12%` of ₹ 10 

= `(6x)/5 xx (12/100 xx 10)`

= `(6x)/5 × 6/5`

= `(36x)/25`

= 1.44x

6. Decrease in annual income

= Old – New 

= 1.6x – 1.44x

= 0.16x

= `(4x)/25`

7. Set decrease = ₹ 120: 

`(4/25)x = 120` 

⇒ `x = 120 xx (25/4)` 

= 30 × 25

= 750

Vimal sold 750 shares.