Question : If a sum of money at simple interest becomes 45 times in 110 years, then in how many years will that sum become 23 times?
Option 1: 48
Option 2: 60
Option 3: 55
Option 4: 50
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Correct Answer: 55
Solution :
Let the principal amount be $P$.
And the rate of interest is $R$.
Case I - The sum of money at simple interest becomes 45 times in 110 years
Amount = Principal + $\frac{\text{Principal × Rate × Time}}{100}$
⇒ $45P = P+\frac{P\times R\times 110}{100}$
⇒ $45 = 1+\frac{110R}{100}$
⇒ $44=\frac{11R}{10}$
⇒ $R=\frac{44\times 10}{11}=40$%
Case II - Now the sum becomes 23 times
Let the time be $T$
⇒ $23P=P+\frac{P\times R\times T}{100}$
⇒ $23-1=\frac{40T}{100}$
⇒ $\frac{22\times 100}{40}=T$
⇒ $T=55$ years
Hence, the correct answer is 55.
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