CAT 2020 Question Paper (Slot 1) - Quant Question 24

Question 24

Veeru invested Rs 10000 at 5% simple annual interest, and exactly after two years, Joy invested Rs 8000 at 10% simple annual interest. How many years after Veeru’s investment, will their balances, i.e., principal plus accumulated interest, be equal?

Correct Answer: 12


Let their individual Amounts be equal after 't' years. Let their initial investments amount to $$A_V$$ and $$A_J$$ ; 

$$A_V\ =10,000\left(1+\frac{5t}{100}\right)$$ and $$A_J\ =8,000\left(1+\frac{10\left(t-2\right)}{100}\right)$$

Equating both: $$10,000\left(1+\frac{5t}{100}\right)\ =8,000\left(1+\frac{10\left(t-2\right)}{100}\right)$$

On simplifying both sides, we get: $$15t\ =\ 180\ ;\ t\ =\ 12$$

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