Question : A sum of INR 900 is divided into two parts such that the interest on the first part at 4% simple interest per annum and that on the other part at 2% simple interest per annum are equal. What is the interest accumulated on each part in a year?
Option 1: INR 18
Option 2: INR 6
Option 3: INR 12
Option 4: INR 20
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Correct Answer: INR 12
Solution : Total sum, $P$ = INR 900 The interest rate on the first part, $R_1$ = 4% The interest rate on the second part, $R_2$ = 2% Time, $n$ = 1 year Let $x$ and $900-x$ be the two parts. Simple interest, SI = $\frac{PnR}{100}$ Simple interest on the first part = simple interest on the second part ⇒ $\frac{x×4×1}{100} = \frac{(900-x)×2×1}{100}$ ⇒ $4x = 1800-2x$ ⇒ $6x=1800$ ⇒ $x=300$ Simple interest in each part = $\frac{x×4×1}{100}$ = $\frac{300×4×1}{100}$ = INR 12 Hence, the correct answer is INR 12.
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