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CAT 2024 Slot 1 QA Question 6

Multiple choice (+3 / −1) · Arithmetic · Simple & Compound Interest · Try it, then check the answer and solution below.

CAT 2024 Slot 1QAArithmetic • Simple & Compound InterestModerate
An amount of Rs 10000 is deposited in bank A for a certain number of years at a simple interest of 5% per annum. On maturity, the total amount received is deposited in bank B for another 5 years at a simple interest of 6% per annum. If the interests received from bank A and bank B are in the ratio 10 : 13, then the investment period, in years, in bank A is
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Answer and solution

Answer: B) 6

📌 Core Concept
The problem involves calculating simple interest for two different periods and rates. The key formula is:
Simple Interest (SI)=P×R×T100\text{Simple Interest (SI)} = \frac{P \times R \times T}{100}
where PP is the principal, RR is the rate, and TT is the time in years.
🔢 Step-by-Step Solution
1
Interest from Bank A:
Principal (P) = Rs 10,000
Rate (R) = 5% per annum
Time (T) = t$ years
Interest (SI_A) = 10000×5×t100\frac{10000 × 5 × t}{100} = 500t$
2
Amount after Bank A:
Amount = Principal + Interest = 10000 + 500t$
3
Interest from Bank B:
Principal (P) = 10000 + 500t$
Rate (R) = 6% per annum
Time (\( T \

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