CAT 2025 Question Paper | Quant Slot 1

CAT Questions

CAT 2025 Quant was dominated by Algebra followed by Arithmetic. In Arithmetic, the questions were dominated by topics like Speed-time-distance, Mixture and Alligations. This year, there was a surprise. The questions from Geometry were relatively on the lower side as compared to the previous years. There were 8 TITA Qs this year. Overall this section was at a medium level of difficulty.

Question 6 : At a certain simple rate of interest, a given sum amounts to Rs 13920 in 3 years, and to Rs 18960 in 6 years and 6 months. If the same given sum had been invested for 2 years at the same rate as before but with interest compounded every 6 months, then the total interest earned, in rupees, would have been nearest to

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Video Explanation

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Explanatory Answer

Let the principal sum be \(P\) and the annual rate of interest be \(R\%\).

Amount after 3 years:
\(A_1=P+\frac{P\times R\times3}{100}=13920\) --- (1)

Amount after 6 years and 6 months (6.5 years):
\(A_2=P+\frac{P\times R\times6.5}{100}=18960\) --- (2)

Subtracting equation (1) from equation (2) to find the interest for 3.5 years:
\(\frac{P\times R\times3.5}{100}=18960-13920=5040\)

Calculating the simple interest per year:
\(\frac{P\times R}{100}=\frac{5040}{3.5}=1440\)

Simple Interest for 3 years = \(1440\times3=4320\)

Finding the principal sum \(P\):
\(P=13920-4320=9600\)

Finding the rate of interest \(R\):
\(R=\frac{1440}{9600}\times100=15\%\) per annum

Now, we calculate the compound interest for 2 years on the same principal \(P\), with interest compounded every 6 months (semi-annually):

The annual rate is \(15\%\), so the semi-annual rate is:
\(r=\frac{15\%}{2}=7.5\%\) per half-year

The number of compounding periods in 2 years is:
\(n=2\text{ years}\times2=4\text{ half-years}\)

Using the compound amount formula:
\(A=9600\left(1+\frac{7.5}{100}\right)^4\)
\(A=9600\times1.075^4\)
\(A=9600\times1.33547=12820.50\)

Calculating the total interest earned:
Compound Interest \(=12820.50-9600=3220.50\approx3221\)

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The answer is '3221'

Choice 4 is the correct answer.

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