Question

Divide Rs. 50,760 into two parts such that if one part is invested in 8% Rs.100 shares at 8% discount and the other in 9% Rs. 100 shares at 8% premium, the annual incomes from both the investments are equal.

Answer 1

Let we divide Rs.50760 in two parts

One is Rs.x and another is Rs.(50760-x)

The share bought with Rs.x were bought at 8% discount$=100-\frac{8}{100}\times 100=Rs.92$

No of share bought with Rs.x=$\frac{x}{92}$

As income =No. of share$\times$dividend $\times$face value

Dividend =8%

Face value=100

$\therefore$ Income$=\frac{x}{92}\times \frac{8}{100}\times 100=\frac{8x}{92}$ (income 1)

The buying price of share bought with Rs.(50760-x) at 8% premium=$100+\frac{8}{100}=\frac{108}{100}$

No of share bought with Rs.(50760-x)=$\frac{50760-x}{108}$

Dividend=9%

Face value=100

$\therefore$ Income$=\frac{50760-x}{108}\times \frac{9}{100}\times 100=\frac{50760-x}{12}$ (income 2)

According to the question both incomes are equal

$\Rightarrow \frac{8x}{92}=\frac{50760-x}{12}$

$\Rightarrow 24x=23(50760-x)$

$\Rightarrow 47x=50760\times 23$

$\Rightarrow x=\frac{50760\times 23}{47}=Rs.24840$

First part=Rs.24840

Another part$=50760-24840=Rs.25920$