RAS question
A sum of money doubles itself in 5 years at simple interest. The rate of interest per annum is:
Correct answer: (B) 20%.
A sum that doubles itself in 5 years at simple interest is earning interest at 20% per annum.
Explanation
When a sum doubles, the amount becomes twice the principal, so the simple interest earned is equal to the principal itself. NCERT defines principal as the borrowed money, interest as the extra money paid for using it, time period as the borrowing period, and rate of interest as a percentage per year. Using the simple-interest relation I = P × R × T / 100, put I = P and T = 5 years: P = P × R × 5 / 100. Cancelling P gives R = 100 / 5 = 20. Therefore, the annual rate is 20%. The same shortcut is: to become n times in T years, R = (n - 1) × 100 / T.
Why the other options are wrong
- (A) 15% for 5 years gives simple interest of 75% of the principal, so the amount would be 1.75 times the principal, not double.
- (C) 25% for 5 years gives simple interest of 125% of the principal, so the amount would exceed double the principal.
- (D) 10% for 5 years gives simple interest of only 50% of the principal, so the amount would be one-and-a-half times the principal.
Concept
This tests the simple-interest formula and the link between amount, principal and interest. It recurs in RAS reasoning and mental ability because percentage-based interest questions reward quick equation setup and cancellation.