Question : The simple interest on a sum of money for 3 years is Rs. 240 and the compound interest on the same sum at the same rate for 2 years is Rs. 170. The rate of interest is:
Option 1: $8$%
Option 2: $29\frac{1}{6}$%
Option 3: $12\frac{1}{2}$%
Option 4: $5\frac{5}{17}$%
Correct Answer: $12\frac{1}{2}$%
Solution :
Simple interest (SI) for 1 year = $\frac{240}{3}$ = Rs. 80
⇒ Simple interest for 2 years = 80 × 2 = Rs. 160
Difference between compound interest (CI) and SI for 2 years = 170 – 160 = Rs. 10 which is interest on Rs. 80
So, $R=\frac{10}{80}$ × 100 = $12\frac{1}{2}$%
Hence, the correct answer is $12\frac{1}{2}$%.
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