Lent at simple interest, a sum of money becomes 3 times itself in 12 years. At the same rate of simple interest, in how many years will the sum become 6 times itself?
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → 30 years
Under simple interest the interest grows by the same amount every year, so the interest is proportional to the time.
Let the sum be \(P\). Becoming \(3P\) means the interest is \(3P-P=2P\) in 12 years
So an interest of \(P\) takes \(\displaystyle \frac{12}{2}=6\) years
Becoming \(6P\) needs an interest of \(6P-P=5P\)
Time \(=5\times6=30\) years
The sum becomes 6 times itself in 30 years.
Why the other options are incorrect
Option (1) 24 years — Incorrect. This doubles the 12 years as if the amount doubled; in 24 years the interest is \(4P\), so the sum becomes only \(5P\).
Option (3) 36 years — Incorrect. In 36 years the interest is \(6P\), so the sum becomes \(7P\), not \(6P\).
Option (4) 18 years — Incorrect. In 18 years the interest is \(3P\), so the sum becomes only \(4P\).