CAT 2021 Slot 2 · Quant · Question 18

CAT 2021 Slot 2 previous year question on Profit and Loss, with the answer and a step-by-step solution.

Profit and LossArithmeticMultiple choiceMedium

Raj invested ₹10000 in a fund. At the end of first year, he incurred a loss but his balance was more than ₹5000. This balance, when invested for another year, grew and the percentage of growth in the second year was five times the percentage of loss in the first year. If the gain of Raj from the initial investment over the two year period is 35%, then the percentage of loss in the first year is

A
15
B
5
C
10
D
70

Pick an option, then check.

Answer & solution

Answer: Option C

Let the first-year loss be 100p percent, so the balance is multiplied by \left( 1-p \right). The second year grows by 500p percent, multiplying by \left( 1+5p \right).

A total gain of 35\% means \left( 1-p \right)\left( 1+5p \right)=1.35.

Expanding: 1+4p-5{p}^{2}=1.35, so 5{p}^{2}-4p+0.35=0, or 100{p}^{2}-80p+7=0.

Then p=\frac{80\pm \sqrt{6400-2800}}{200}=\frac{80\pm 60}{200}, giving p=0.7 or p=0.1.

Here is where the balance condition earns its place: p=0.7 would leave only ₹3000, which is less than ₹5000. So p=0.1 and the first-year loss is 10\%.

CAT 2021 Slot 2 · Quant · Question 18

More Profit and Loss questions