Question

\[P = Rs.8500,A = Rs.10,200,R = 12\dfrac{1}{2}\% \] SI, t will be .
A) I yr. 7 mth.
B) 2 yrs.
C) \[1\dfrac{1}{2}\]yr.
D) None of these.

Answer 1

Hint:
Here in the question we have given the principal amount, rate of interest and time. We have been asked to find the time in which the principal amount will become the given amount. We can use the following formula and solve it for known t.
\[A = {\text{ }}P\left( {1 + \dfrac{{rt}}{{100}}} \right)\]
Here, A= final amount
           p= initial principal
           r=annual interest rate in percent
           T= time period (in years)

Complete step by step solution:
Given; Principal = Rs.8500
            Amount= Rs. 10,200
 Rate of interest= \[12\dfrac{1}{2}\% \]
Let (t) be the time period for which amount is to be calculated on Simple Interest (S.I).
Using formula; \[Amount = {\text{ }}Principal\left( {1 + \dfrac{{rt}}{{100}}} \right)\]
Where, r= rate of interest in percent
              t= time period in years.
\[
   \Rightarrow 10,200 = 8500\left( {1 + \dfrac{{\dfrac{{25}}{2} \times t}}{{100}}} \right) \\
   \Rightarrow \dfrac{{10,200}}{{8500}} = \left( {1 + \dfrac{{25 \times t}}{{200}}} \right) \\
   \Rightarrow \dfrac{{10,2}}{{85}} - 1 = \dfrac{t}{8} \\
\]
\[ \Rightarrow \dfrac{{17}}{{85}} = \dfrac{t}{8}\]
\[
   \Rightarrow \dfrac{1}{5} = \dfrac{t}{8} \\
   \Rightarrow t = \dfrac{8}{5} \\
\]

Required time period is \[\dfrac{8}{5}\]years \[ = 1\dfrac{3}{5}years\]
Option (D) is correct.

Note:
Simple Interest: It is calculated on the principal, or original, amount of a loan. While putting values in above formula keep in mind that the rate of interest must be in percent and time period must be in years.