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CAT 2020 Slot 2 QA Question & Solution

ArithmeticEasy

Question

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

Solution

For two years the compound interest is $\frac{PR(1)}{100}+\frac{PR(1)}{100}\left(1+\frac{PR(1)}{100}\right)$

For three years the simple interest is $\frac{9PR}{100}$

Now R(1)= 5% and R=3%

Hence $\frac{5P}{100}+\frac{5P}{100}\left(1.05\right)-\frac{9P}{100}=1125$

$\frac{-4P}{100}+\frac{5.25P}{100}=1125$

$\frac{1.25P}{100}=1125$

Solving we get P= 90000