CAT 2022 Slot 1 · Quant · Question 16

Let the two parts be {P}_{1} and {P}_{2}.

Simple interest is principal times rate times time, divided by 100.

The first part earns \frac{{P}_{1}\times 15\times 4}{100}.

The second earns \frac{{P}_{2}\times 12\times 3}{100}.

These are equal, so 60{P}_{1}=36{P}_{2}.

Dividing both sides by 12, 5{P}_{1}=3{P}_{2}.

So \frac{{P}_{1}}{{P}_{2}}=\frac{3}{5}.

The two parts are therefore in the ratio 3:5, making 8 parts in all.

The first part is \frac{3}{8} of the savings.

As a percentage, \frac{3}{8}=0.375, that is 37.5% — the second option.

Shortcut. Equal interest means the principals are inversely proportional to the rate-times-time products, 60 and 36. So {P}_{1}:{P}_{2}=36:60=3:5, and the first share is \frac{3}{8} — a fraction worth knowing as 37.5%.