Question : A sum of Rs. 400 becomes Rs. 448 at simple interest in 2 years. In how many years will the sum of Rs. 550 amounts to Rs. 682 at the same rate?
Option 1: 2 years
Option 2: 3 years
Option 3: 3.5 years
Option 4: 4 years
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Correct Answer: 4 years
Solution : Interest for 2 years = Rs. (448 – 400) = Rs. 48 i.e. 1 year interest = $\frac{48}{2}$ 1 year interest = Rs. 24 We know Rate of interest = $\frac{\text{Simple interest} \times 100}{\text{Principal × Time}} = \frac{48 \times 100}{400 \times 2} = 6$% Principal = Rs. 550 Amount = Rs. 682 SI = Rs. 682 – Rs. 550 = Rs. 132 Time = $\frac{\text{SI} \times 100}{PR} = \frac{132 \times 100}{550 \times 6} = 4$ years. Hence, the correct answer is 4 years.
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