At a certain rate of simple interest, a certain sum doubles itself in 10…
2025
At a certain rate of simple interest, a certain sum doubles itself in 10 years. In how many years will it become triple?
- A.
30
- B.
40
- C.
15
- D.
None of these
Show answer & explanation
Correct answer: D
Concept: In Simple Interest, the interest earned is directly proportional to time (for a fixed principal and rate). So if a sum takes T₁ years to earn its own value as interest (i.e., double itself), the same sum will take twice that time to earn twice that interest (i.e., triple itself).
Application: Let the principal be P and rate be R% per annum.
The sum doubles in 10 years, so the interest earned in 10 years equals the principal: SI = P.
Using SI = (P × R × T)/100: P = (P × R × 10)/100, which gives R = 10% per annum.
To triple the sum, the interest required is 2P (since the sum becomes 3P, i.e., 2P more than the principal).
Using the same formula: 2P = (P × 10 × T)/100, so T = (2 × 100)/10 = 20 years.
Cross-check: At 10% simple interest, in 20 years the interest = (P × 10 × 20)/100 = 2P, so the amount = P + 2P = 3P — confirming the sum triples in 20 years.
Since 20 years is not among the numeric options offered (30, 40, 15), the correct choice is "None of these."