Question

A man invests a certain sum of money in 6% hundred-rupee shares at Rs. 12 premium. When the shares fell to Rs. 96, he sold out all the shares bought and invested the proceed in 10%, ten-rupee shares at Rs. 8. If the change in his income is Rs. 540, find the sum invested originally.

Answer 1

Let the original sum invested = x 

The number of Rs. 100 shares purchased at premium of Rs. 12

= `x/(100 + 12)`

= `x/112`

The income per original share at 6% = Rs. 6

Total Income = (Number of shares) × (Earning per share)

= (Number of shares) × 6

= `x/112 xx 6`

= `(3x)/56`

Proceeds from sale of original share at Rs. 96 per share

= (Number of shares) × 96

= `x/112 xx 96`

= `(6x)/7`

Number of Rs. 10 shares purchased at Rs. 8 per share from proceeds of original shares

= `"Proceeds from sale of original shares"/8`

= `((6x)/7)/8`

= `(3x)/28`

Income per new share Rs. 10 at 10%

= `10/100 xx 10`

= Rs. 1

Total income from new shares

= (Number of shares) × (Income per share)

= `(3x)/28 xx 1`

= `(3x)/28`

Given change in income = 540

Income from old shares – Income from new shares = 540

∴ `540 = (3x)/28 - (3x)/56 = (3x)/56`

∴ x = `540/(3/56)` = 10,080

Thus, the original sum invested is Rs. 10,080.