Question : At a certain rate of simple interest per annum, a certain sum amounts to INR 24,000 in 7 years and to INR 32,000 in 12 years. What is the rate of simple interest paid per annum?
Option 1: 15%
Option 2: 25%
Option 3: 12.5%
Option 4: 20%
Correct Answer: 12.5%
Solution :
Given: At a certain rate of simple interest per annum, a certain sum amounts to INR 24,000 in 7 years and to INR 32,000 in 12 years.
So, simple interest of 5 years = INR 32000 – INR 24000 = INR 8,000
$\therefore$ Simple interest of 1 year = $\frac{ 8000}{5}$ = INR 1,600
⇒ Simple interest of 7 years = 1600 × 7 = INR 11,200
Principal = The amount in 7 years – The simple interest of 7 years = 24000 – 11200 = INR 12,800
We know, Simple interest = $\frac{\text{Principal × Rate × Time}}{100}$
⇒ $11200=\frac{12800\times \text{Rate}\times 7}{100}$
⇒ Rate $=\frac{11200\times 100}{12800\times 7}=12.5\%$
Hence, the correct answer is 12.5%.
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