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# A sum of money at simple interest becomes 1.5 times of itself in 3 years. In how many years will the same treble itself?A.10 yearsB.11 yearsC.12 yearsD.13 years

Last updated date: 25th Jun 2024
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Hint: Simple interest is a quick and easy method of calculating the interest charge on a loan. Simple interest is determined by multiplying the daily interest rate by the principal by the number of days that elapse between payments.

Complete step by step solution:
According to the question,
Let the initial amount be P and the rate be R%.
Then from the formula of Simple Interest we can write:
$S.I = P \times \dfrac{R}{{100}} \times Time$
Therefore the amount will be: $= P + S.I$
$\therefore this \Rightarrow A = P + S.I \\ \Rightarrow A = P + P \times \dfrac{R}{{100}} \times T \\ \Rightarrow A = P(1 + \dfrac{{RT}}{{100}}) \\$
Now according to the question the sum P is increased 1.5 times in 3 years
Therefore $A = 1.5P$
$this \Rightarrow A = 1.5P \\ \Rightarrow 1.5P = P(1 + \dfrac{{3R}}{{100}}) \\ \Rightarrow 1.5 = 1 + \dfrac{{3R}}{{100}} \\ \Rightarrow 0.5 = \dfrac{{3R}}{{100}} \\ \Rightarrow R = \dfrac{{50}}{3} \\$
Now, in the second part the amount becomes 3 times of the sum in T years.
Therefore
$A = 3P \\ \Rightarrow 3P = P(1 + \dfrac{{RT}}{{100}}) \\ \Rightarrow 3 = 1 + \dfrac{{\dfrac{{50}}{3}T}}{{100}} \\ \Rightarrow 2 = \dfrac{{50}}{{300}}T \\ \Rightarrow 2 = \dfrac{1}{6}T \\ \Rightarrow 12 = T \\ \Rightarrow T = 12years \\$
Hence the required time period is equal to 12 years.

Note: Sometimes to create confusion time is converted in other units like in one part it is given in years but in other it is in months , so be careful about this to convert everything in one unit and then proceed.