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

Then the number of Rs 100 shares purchased at the premium of Rs 12

`= x/(100 + 12) = x/112`

The income per original shares at 6% = Rs 6

Total income = (Number of shares) x  (earning per share)

`= ("Number of shares") xx 6 = x/122 xx 6 = (3x)/56` 

Proceeds from sale of original shares at Rs 96 per share

`= ("Number of shares") xx 96 = x/112 xx 96 = (6x)/7` 

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

`= ("Proceeds from sale of orignal shares")/8 = ((6x)/7)/8 = (3x)/28`

Income per new share of 10 at 10% = 10/100 xx 10 = Rs 1

Total income from new shares

`= "(Number of shares)" xx "(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`

`:. x = 540/(3/56)= 10080`

Thus the original sum invested is Rs 10080