RAS question
A sum of money becomes double in 5 years at simple interest. The rate of interest per annum is:
Correct answer: (B) 20%.
A sum that doubles in 5 years at simple interest earns interest equal to the principal, so the annual rate of interest is 20%.
Explanation
In simple interest, NCERT defines principal as the borrowed money, interest as the extra money paid for using it, and amount as principal plus interest. Here the amount becomes double the principal in 5 years, so the interest earned is exactly equal to the principal. Using the simple-interest formula SI = P x R x T / 100, put SI = P and T = 5. This gives P = P x R x 5 / 100. Cancelling P leaves 1 = 5R/100, so 5R = 100 and R = 20. Therefore, the required rate is 20% per annum. The same result follows from the general rule: for a sum to become n times in T years at simple interest, Rate = (n - 1) x 100 / T.
Why the other options are wrong
- (A) At 15% per annum for 5 years, simple interest would be 75% of the principal, so the amount would not become double.
- (C) At 25% per annum for 5 years, simple interest would be 125% of the principal, which is more than the interest needed for doubling.
- (D) At 10% per annum for 5 years, simple interest would be only 50% of the principal, leaving the amount below double.
Concept
This tests simple interest under Comparing Quantities: recognising that a doubled amount means interest equals principal, then applying SI = P x R x T / 100. It recurs in RAS mental ability because it rewards quick formula use and percentage reasoning without lengthy computation.