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CAT Exam 2021 Slot 3 Solved Paper

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Question : 60 of 66

Marks: +1, -0

Bank A offers 6% interest rate per annum compounded half-yearly. Bank B and Bank C offer simple interest but the annual interest rate offered by Bank C is twice that of Bank B. Raju invests a certain amount in Bank B for a certain period and Rupa invests ₹ 10,000 in Bank C for twice that period. The interest that would accrue to Raju during that period is equal to the interest that would have accrued had he invested the same amount in Bank A for one year. The interest accrued, in INR, to Rupa is

3436
2436
2346
1436

Solution:

Bank A: 6% p.a. 1/2 yearly (CI)

Bank B: x% p.a (SI)

Bank C: 2x% p.a (SI)

Let Raju invest

\text{Rs } P

in bank B for

t \text{ years}

. Hence, Rupa invests

\text{Rs } 10{,}000

in bank C for

2t \text{ years}

.

Now,

\frac{P \frac{x}{100}}{t} = P \left(1 + \frac{3}{100}\right)^2 - P

\frac{\frac{x}{100}}{t} = 1.0609 - 1

\frac{\frac{x}{100}}{t} = 0.0609

We need to calculate

SI

= 10000 \times 2t \times \frac{2x}{100} = 40000 \frac{x}{100} t = 40000 \times 0.0609 = 2436

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