A certain sum of money becomes seven times itself when invested at a certain rate of simple interest, in 14 years. How much time (in years, rounded off to 2 decimal places) will it take to become 18 times itself at the same rate?
Show answer & explanation
Correct answer: B
Explanation
The correct answer is Option 2 i.e. 39.67.
We know that,
A = P(1 + RT)
here, A = Amount, P = Principal, R = Rate, and T = Time
A certain sum of money becomes seven times itself
⇒ A = 7P
⇒ 7P 7= P(1 + R × 14)
⇒ 7 = (1 + 14R)
⇒ 14R = 6
⇒ R = 3/7
Now, the amount becomes 18 times itself
⇒ A = 18P
⇒ A = P(1 + RT)
⇒ 18P = P(1 + 3/7 × T)
⇒ 18 = 1 + 3T/7
⇒ 3T/7 = 18 - 1
⇒ 3T/7 = 17
⇒ T = (17 × 7)/3
⇒ T = 119/3 = 39.67 years