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Principal Amount from CI and SI

CAT 2020 Slot 2 · Quantitative Ability · Easy · Arithmetic

This is an easy Quantitative Ability question from the CAT 2020 Slot 2 paper. It tests Arithmetic. The full answer key and a step-by-step explanation are below — try it yourself first, then reveal the solution.

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For the same principal amount, the compound interest for two years at 5%5\% per annum exceeds the simple interest for three years at 3%3\% per annum by Rs 1125. Then the principal amount in rupees is

Answer

90000

Explanation

Let the principal amount be PP. Compound interest for 2 years at 5%5\%: CI=P(1+5100)2−P=P(1.1025−1)=0.1025P\text{CI} = P \left(1 + \frac{5}{100}\right)^2 - P = P(1.1025 - 1) = 0.1025 P Simple interest for 3 years at 3%3\%: SI=P×3×3100=0.09P\text{SI} = P \times \frac{3 \times 3}{100} = 0.09 P Given CI−SI=1125\text{CI} - \text{SI} = 1125: 0.1025P−0.09P=11250.1025 P - 0.09 P = 1125 0.0125P=11250.0125 P = 1125 P=11250.0125=90000P = \frac{1125}{0.0125} = 90000

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