CAT 2024 Question Paper | Quant Slot 3

CAT Questions

CAT 2024 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 11 Aman invests Rs 4000 in a bank at a certain rate of interest, compounded annually. If the ratio of the value of the investment after 3 years to the value of the investment after 5 years is 25 : 36, then the minimum number of years required for the value of the investment to exceed Rs 20000 is

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Video Explanation

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Explanatory Answer

\[ \frac{4000 \times\left[1+\frac{r}{100}\right]^3}{4000 \times\left[1+\frac{r}{100}\right]^5}=\frac{25}{36} \] Solving this, we get:
\[ \begin{array}{l} 1+\frac{r}{100}=\frac{6}{5} \\ r=20 \% \end{array} \] Now,
\[ \begin{array}{l} 4000 \times\left[1+\frac{20}{100}\right]^n>20000 \\ \text { i.e., } 1.2^n>5 \\ \Rightarrow n=9 \end{array} \]

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The question is "Aman invests Rs 4000 in a bank at a certain rate of interest, compounded annually. If the ratio of the value of the investment after 3 years to the value of the investment after 5 years is 25 : 36, then the minimum number of years required for the value of the investment to exceed Rs 20000 is"

Hence, the answer is '9'

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