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

= ${\displaystyle \frac{x}{100+12}}$

= ${\displaystyle \frac{x}{112}}$

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

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

= (Number of shares) × 6

= ${\displaystyle \frac{x}{112}\times 6}$

= ${\displaystyle \frac{3x}{56}}$

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

= (Number of shares) × 96

= ${\displaystyle \frac{x}{112}\times 96}$

= ${\displaystyle \frac{6x}{7}}$

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

= ${\displaystyle \frac{\text{Proceeds from sale of original shares}}{8}}$

= ${\displaystyle \frac{\frac{6x}{7}}{8}}$

= ${\displaystyle \frac{3x}{28}}$

Income per new share Rs. 10 at 10%

= ${\displaystyle \frac{10}{100}\times 10}$

= Rs. 1

Total income from new shares

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

= ${\displaystyle \frac{3x}{28}\times 1}$

= ${\displaystyle \frac{3x}{28}}$

Given change in income = 540

Income from old shares – Income from new shares = 540

∴ ${\displaystyle 540=\frac{3x}{28}-\frac{3x}{56}=\frac{3x}{56}}$

∴ x = ${\displaystyle \frac{540}{\frac{3}{56}}}$ = 10,080

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