Question : A sum of Rs. 500 becomes Rs. 580 at simple interest in 2 years. In how many years will the sum of Rs. 650 amounts to Rs. 858 at the same rate of simple interest?
Option 1: 4 years
Option 2: 8 years
Option 3: 5 years
Option 4: 6 years
Correct Answer: 4 years
Solution :
Given: A sum of Rs. 500 becomes Rs. 580 at simple interest in 2 years.
Principal ($P$) = Rs. 500
Simple interest ($I$) = 580 – 500 = Rs. 80
Time ($T$) = 2 years
So, the rate of interest ($R$) = $\frac{100×I}{P×T}$ = $\frac{100×80}{500×2}$ = 8%
Now, at the same interest rate,
Principal ($P$) = Rs. 650
Total interest ($I$) = (858 – 650) = 208
The rate of interest ($R$) = 8%
So, the required time ($T$) = $\frac{100×I}{P×R}$ = $\frac{100×208}{650×8}$ = 4 years
Hence, the correct answer is 4 years.
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