CAT 2022 Slot 3 · Quant · Question 9

CAT 2022 Slot 3 previous year question on Simple Interest and Compound Interest, with the answer and a step-by-step solution.

Simple Interest and Compound InterestArithmeticMultiple choiceMedium

Nitu has an initial capital of ₹20,000. Out of this, she invests ₹8,000 at 5.5% in bank A, ₹5,000 at 5.6% in bank B and the remaining amount at x% in bank C, each rate being simple interest per annum. Her combined annual interest income from these investments is equal to 5% of the initial capital. If she had invested her entire initial capital in bank C alone, then her annual interest income, in rupees, would have been

A
900
B
700
C
1000
D
800

Pick an option, then check.

Answer & solution

Answer: Option D

Her target income is 5% of ₹20000, that is 0.05\times 20000=1000.

Bank A holds ₹8000 at 5.5%, yielding 8000\times 0.055=440.

Bank B holds ₹5000 at 5.6%, yielding 5000\times 0.056=280.

Those two together give 440+280=720.

So bank C must supply 1000-720=280.

The amount in bank C is 20000-8000-5000=7000.

Its rate is therefore \frac{280}{7000}=0.04, that is 4% per annum.

Investing the whole ₹20000 at that rate would yield 20000\times 0.04=800.

So the income would have been ₹800 — the fourth option.

Shortcut. Bank C's rate is below the 5% blended target while A and B are above it, so the answer must fall under ₹1000 — which already eliminates option 3. The arithmetic then needs only the single subtraction 1000-720.

CAT 2022 Slot 3 · Quant · Question 9

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