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Question

Divide Rs.101520 into two parts such that if one part is invested in 8%,Rs 100 shares at 8% discount and the other 9%,Rs 50 shares at 8% premium, the annual incomes are equal.

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Solution

We first determine the price at which each of the shares can be purchased and the annual income form each share.
Let P100be the purchase price of th Rs.100 share.
Let P100 be the income form one R.s100 share.
Let P50 be the purchase price of the Rs.50 share.
Let I50be 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 ;
P100=100(100×0.08)=92
The Rs.50 price can be purchased at a premium of 8%, hence the price is
P50=50+(50×0.8)=54
The income form the R.s100 share will be:
I100=100×0.08
The income from the Rs.50 share will be
I50=50×0.09=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=84.5=1.777
Now, we can determine the purchase price of 1.7777 Rs.50 share as
1.777×54=96 (approx)
Let X be the number of Rs.100 shares purchased.
92x+96x=1015204
x=540

Hence, the amount to be invested in each types of share will be
92×540=49680 in rs.100 shares and
54×540=51840 in rs.50 shares

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