CAT 2023 Question Paper | Quant Slot 1

CAT Questions

CAT 2023 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 16 : Anil invests Rs. 22000 for 6 years in a certain scheme with 4% interest per annum, compounded half-yearly. Sunil invests in the same scheme for 5 years, and then reinvests the entire amount received at the end of 5 years for one year at 10% simple interest. If the amounts received by both at the end of 6 years are same, then the initial investment made by Sunil, in rupees, is

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Video Explanation

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Explanatory Answer

“Anil invests Rs. 22000 for 6 years in a certain scheme with 4% interest per annum, compounded half-yearly.”

Total Amount of Anil’s investment after 6 years = \( 22000 \times \left( 1 + \frac { 2 } { 100 } \right) ^ { 12 } = 22000 \times 1.02 ^ { 12 } \)
Let Sunil Invest a Principal of P.
“Sunil invests in the same scheme for 5 years, and then reinvests the entire amount received at the end of 5 years for one year at 10% simple interest.”
Total Amount of Sunil’s investment after 6 years = \( P \times \left( 1 + \frac { 2 } { 100 } \right) ^ { 10 } \times 1.1 = P \times 1.02 ^ { 10 } \times 1.1 \)
“…the amounts received by both at the end of 6 years are same…”
\( 22000 \times 1.02 ^ { 12 } = P \times 1.02 ^ { 10 } \times 1.1 \)
\( P = \frac { 22000 \times 1.02 ^ { 2 } } { 1.1 } = 20808 \)
Therefore, Sunil’s investment is Rs. 20808

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The answer is '20808'