A sum of money at simple interest becomes 4 times itself in 15 years. In how many years will it become 7 times itself at the same rate?
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → 30 years
Becoming 4 times means the interest is 3 times the sum. Simple interest grows evenly with time, so the time is proportional to the interest, not to the final multiple.
Interest in 15 years \(=4-1=3\) times the sum
Interest needed \(=7-1=6\) times the sum
Time \(\displaystyle =15\times\frac{6}{3}=30\) years
The sum becomes 7 times itself in 30 years.
Why the other options are incorrect
Option (1) 35 years — Incorrect. In 35 years the interest would be \(7\) times the sum, so the sum would become 8 times itself, not 7.
Option (2) 25 years — Incorrect. In 25 years the interest would be \(5\) times the sum, so the sum would become 6 times itself, not 7.
Option (3) 26.25 years — Incorrect. In 26.25 years the interest would be \(5.25\) times the sum, so the sum would become 6.25 times itself, not 7.