Question : If a sum of money becomes Rs. 4000 in 2 years and Rs. 5500 in 4 years and 6 months, at the same rate of simple interest per annum, the rate of simple interest is:
Option 1: $21\frac{3}{7}$%
Option 2: $21\frac{2}{7}$%
Option 3: $21\frac{1}{7}$%
Option 4: $21\frac{5}{7}$%
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Correct Answer: $21\frac{3}{7}$%
Solution :
Given: The sum of money becomes Rs. 4000 in 2 years and Rs. 5500 in 4 years and 6 months, at the same rate of simple interest.
Simple interest of 2 years 6 months = 5500 – 4000 = 1500
Simple interest of 1 year = $1500×\frac{2}{5} =600$
Simple interest of 2 years = 600 × 2 = 1200
So, principal = 4000 – 1200 = 2800
Simple interest = $\frac{\text{Principal×Rate×Time}}{100}$
⇒ 1200 = $\frac{2800×r×2}{100}$
∴ $r=21\frac{3}{7}$%
Hence, the correct answer is $21\frac{3}{7}$%.
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