Question

Divide Rs.$101520$ into two parts such that if one part is invested in $8\%,Rs100$ shares at $8\%$ discount and the other $9\%,Rs50$ shares at $8\%$ premium, the annual incomes are equal.

Answer 1

We first determine the price at which each of the shares can be purchased and the annual income form each share.

Let $P_{100}$be the purchase price of th $Rs.100$ share.

Let $P_{100}$ be the income form one $R.s100$ share.

Let $P_{50}$ be the purchase price of the $Rs.50$ share.

Let $I_{50}$be the income form one $Rs.50$ share.

Since the $Rs/100$ share can be purchased at a discount of $8\%$, the purchase price will be ;

$P_{100}=100-\left(100\times 0.08\right)=92$

The $Rs.50$ price can be purchased at a premium of $8\%$, hence the price is

$P_{50}=50+\left(50\times 0.8\right)=54$

The income form the $R.s100$ share will be:

$I_{100}=100\times 0.08$

The income from the $Rs.50$ share will be

$I_{50}=50\times 0.09=4.5$

since the question states that the income from both types of share must be equal, we can determine the number of $Rs.50$ share to earn the same income from one $Rs.100$ share.

$4.5x=8$

$x=\frac{8}{4.5}=1.777$

Now, we can determine the purchase price of $1.7777$ $Rs.50$ share as

$1.777\times 54=96$ (approx)

Let $X$ be the number of $Rs.100$ shares purchased.

$92x+96x=101520$4

$x=540$

Hence, the amount to be invested in each types of share will be

$92\times 540=49680$ in $rs.100$ shares and

$54\times 540=51840$ in $rs.50$ shares