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CAT 2022 Slot 2 — QA Question 7

Simple InterestEasy

Mr. Pinto invests one-fifth of his capital at 6%, one-third at 10% and the remaining at 1%, each rate being simple interest per annum. Then, the minimum number of years required for the cumulative interest income from these investments to equal or exceed his initial capital is

Answer & solution

Answer: 20

Solution

Easy

Simple interest is linear in time, so total annual interest is fixed. Pick a convenient capital that splits cleanly into fifths and thirds, compute the yearly interest, then divide the capital by it to find the years needed to recover the whole capital.

1

Choose capital =Rs. 1500=\text{Rs. }1500 (divisible by 55 and 33). The three parts are:

15⋅1500=300,13⋅1500=500,rest=1500−800=700.\tfrac15\cdot1500=300,\quad \tfrac13\cdot1500=500,\quad \text{rest}=1500-800=700.
2

Interest per year from each part:

6% of 300=1810% of 500=501% of 700=7Total=18+50+7=75 per year.\begin{aligned} &6\%\text{ of }300=18\\ &10\%\text{ of }500=50\\ &1\%\text{ of }700=7\\ &\text{Total}=18+50+7=75\ \text{per year.} \end{aligned}
3

Years to make interest ≥\ge capital:

150075=20.\frac{1500}{75}=20.

Minimum number of years =20=\mathbf{20}.

CAT 2022 Slot 2 QA Q7: Mr. Pinto invests one-fifth of his capital at 6%, one-third at 10% and the remaining at 1%, each rate being si — Solution | TheCATExam