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
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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