Question
Download Solution PDFThe amount doubles itself under Simple Interest in 2.5 years. In how many years will it become 45 times of itself?
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFGiven:
Under Simple Interest (SI), the amount doubles in 2.5 years.
Formula used:
Amount = Principal + Simple Interest
Simple Interest (SI) = Principal × Rate × Time / 100
Calculations:
When the amount doubles, SI = Principal.
⇒ Principal × Rate × Time / 100 = Principal
⇒ Rate × Time / 100 = 1
⇒ Rate × 2.5 = 100
⇒ Rate = 40%
To calculate the time for the amount to become 45 times of itself:
⇒ SI = Principal × (45 - 1)
⇒ Principal × Rate × Time / 100 = Principal × 44
⇒ Rate × Time / 100 = 44
⇒ 40 × Time / 100 = 44
⇒ Time = (44 × 100) / 40
⇒ Time = 110 years
∴ The correct answer is option (3).
Shortcut TrickLet the principal amount be P.
The amount doubles itself, meaning it becomes 2P.
Increases 2P - P = P
P increases in 2.5 years
And amount becomes 45 times
Increases 45P - P = 44P
So, 44P increases in (2.5 × 44) / 1 = 110 years.
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