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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