Question

By selling at Rs. 92, some 2.5% Rs. 100 shares and investing the proceeds in 5% Rs. 100 shares at Rs. 115, a person increased his annual income by Rs. 90. Find:

1. the number of shares sold.
2. the number of shares purchased.
3. the new income.
4. the rate percent which he earns on his investment.

Answer 1

Rate of dividend = 2.5% and market price = Rs. 92

Let number of shares purchased = x.

Selling price of x shares = 92 x

Income from investing

₹ x = `(92x xx 2.5)/(92)`

= `(92 xx x 25)/(92 xx 10)`

= `(5)/(2)x`

Again by investing 92 x in 5% at ₹ 115

the dividend = `(92x xx 5)/(115)` = 4x

Difference = `4x - (5)/(2)x = (3)/(2)x`

∴ `(3)/(2)x` = 90

⇒ x = `(90 xx 2)/(3)` = 60

(i) No. of shares = 60

(ii) No. of shares sold = `(92x)/(115)`

= `(92 xx 60)/(115)`

= 48

(iii) New income = 4x = 4 × 60

= ₹ 240

(iv) Rate percent interest on investment

= `(5 xx 100)/(115)`

= `(100)/(23)`

= `4(8)/(23)`%.