A sum of money doubles in 14 years. In how many years would it triple if the…
2023
A sum of money doubles in 14 years. In how many years would it triple if the rate of interest is simple?
Answer: B. 28 years — ConceptUnder simple interest, interest grows in direct proportion to time when the principal and annual rate stay fixed. If the interest earned in one time…
- A.
25 years
- B.
28 years
- C.
18 years
- D.
33 years
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Show answer & explanation
Correct answer: B
Concept
Under simple interest, interest grows in direct proportion to time when the principal and annual rate stay fixed.
If the interest earned in one time interval is known, earning twice that interest requires twice the interval.
Application
Let the principal be P. Doubling the amount in 14 years means the interest earned in 14 years is P.
Tripling the amount means the final amount is 3P, so the required interest is 3P − P = 2P.
Because simple interest is proportional to time, t/14 = 2P/P = 2.
Therefore, t = 14 × 2 = 28 years.
Cross-check
In 28 years, the time is twice 14 years, so simple interest is twice P, namely 2P. The amount is then P + 2P = 3P, confirming 28 years.