Question

Divide ₹$40,608$ such that if one part is invested in $8$%, ₹$100$ shares at $8$% discount and the second part is invested in $9$%, ₹$100$ shares at $8$% premium, then the annual income from both the investments are equal.
[4 Marks]

Answer 1

Let the two part be ₹$x$ and ₹$(40,608-x)$.

Considering the first part of the investment, ₹$x$
Face value of each share $=$ ₹$100$
Market value of each share
$=$ Face value $-$ Discount
$=$ ₹$100$ $-$ $8$% of ₹$100$ = ₹$92$
Number of shares bought $=\frac{Investment}{Marketvalue}$ $=\frac{x}{92}$
Total dividend
$=$ Number of shares $\times$ Rate of dividends $\times$ Face value
$=\frac{x}{92}$ $\times$ $8$% $\times$ ₹$100$ $=$₹$\frac{2x}{23}$
(1.5 Marks)

Considering the second part of the investment, ₹$(40,608-x)$
Face value of each share = ₹$100$
Market value of each share
$=$ Face value $+$ Premium
= ₹$100+8$% of ₹$100$ = ₹$108$
Number of share bought $=\frac{Investment}{Marketvalue}$ $=\frac{(40,608-x)}{108}$
Total dividend
$=$ Number of shares $\times$ Rate of dividends $\times$ Face value
$=\frac{(40,608-x)}{108}$ $\times$ $9$% $\times$ ₹$100$ $=$₹$\frac{(40,608-x)}{12}$
(1.5 Marks)

Given that dividend from both the investment are equal.
So, $\frac{2x}{23}=\frac{(40,608-x)}{12}$
$\therefore$ $x=19,872$
$(40,608-x)=40,608-19,872$ $=20,736$
(1 Mark)

So, the two investments are ₹$19,872$ and ₹$20,736$.