Question : Sumit lent INR 5000 to Ram for 2 years and INR 8000 to Mayur for 3 years on simple interest at the same rate of interest and received INR 1700 in total from both of them as interest. What is the rate of interest per annum?
Option 1: 8%
Option 2: 4%
Option 3: 5%
Option 4: 10%
Correct Answer: 5%
Solution :
Principal sum, $P_1$ = INR 5000
Term, $n_1$ = 2 years
Principal sum, $P_2$ = INR 8000
Term, $n_2$ = 3 years
Simple interest, SI = INR 1700
Let $R$ be the rate of interest.
SI = $\frac{P_1 × R × n_1}{100} + \frac{P_2 × R × n_2}{100}$
$⇒1700 = \frac{5000 × R × 2}{100} + \frac{8000 × R × 3}{100}$
$⇒170000 = 10000R + 24000R$
$⇒R = \frac{170000}{34000}$
$\therefore R= 5\%$
Hence, the correct answer is 5%.
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