Question : A sum becomes Rs.15,500 in 7 years on simple interest at the rate of 30 percent per annum. What is the total interest for the 7 years?
Option 1: Rs. 12,200
Option 2: Rs. 1,47,000
Option 3: Rs. 10,500
Option 4: Rs. 11,500
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Correct Answer: Rs. 10,500
Solution :
Given, Sum= Rs. 15500
Rate of interest (r) = 30% per annum
Time (t) = 7 years
Let the principal be P.
⇒ [P + (simple interest)] = sum
⇒ [P + $\frac{\text{Prt}}{100}$] = sum
⇒ [P + $\frac{\text{P} × 30 × 7}{100}$] = 15500
⇒ [P + $\frac{\text{P} × 210}{100}$] = 15500
⇒ [P + $\frac{\text{21P}}{10}$] = 15500
⇒ $\frac{31\text{P}}{10}$ = 15500
⇒ P = $15500 × \frac{10}{31}$
⇒ P = 5000
Simple interest = 15500 – 5000 = Rs. 10500
Hence, the correct answer is Rs. 10500.
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