A sum of money at simple interest becomes 5 times itself in 12 years. In how many years will it become 8 times itself at the same rate?
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → 21 years
Becoming 5 times means the interest is 4 times the sum. Simple interest grows evenly with time, so the time is proportional to the interest, not to the final multiple.
Interest in 12 years \(=5-1=4\) times the sum
Interest needed \(=8-1=7\) times the sum
Time \(\displaystyle =12\times\frac{7}{4}=21\) years
The sum becomes 8 times itself in 21 years.
Why the other options are incorrect
Option (1) 19.2 years — Incorrect. In 19.2 years the interest would be \(6.4\) times the sum, so the sum would become 7.4 times itself, not 8.
Option (2) 18 years — Incorrect. In 18 years the interest would be \(6\) times the sum, so the sum would become 7 times itself, not 8.
Option (4) 24 years — Incorrect. In 24 years the interest would be \(8\) times the sum, so the sum would become 9 times itself, not 8.