Question
Download Solution PDFThe amount doubles itself under Simple interest in 3 years. In how many years will it become 52 times of itself?
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFGiven:
The amount doubles itself under Simple Interest in 3 years.
Formula used:
Simple Interest (SI) = P × R × T / 100
Total Amount (A) = P + SI
Calculations:
Let the principal amount be P.
In 3 years, the amount doubles, so A = 2P.
SI = A - P = 2P - P = P
P = P × R × 3 / 100
⇒ R = 100 / 3 %
We need to find the time (T) for the amount to become 52 times of itself.
So, A = 52P
SI = A - P = 52P - P = 51P
Using the formula for Simple Interest:
51P = P × (100 / 3) × T / 100
⇒ 51 = (100 / 3) × T / 100
⇒ T = 51 × 3
⇒ T = 153 years
∴ The correct answer is option (3).
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