Question

Himanshu borrowed Rs.12,000 at the rate of simple interest \[15\dfrac{1}{2}%\] for certain years. At the end of the period, he paid a total sum of Rs. 20,370. Find the time period.

Answer 1

Hint: To solve the question, we have to apply the appropriate formulae of simple interest. To calculate the time period substitute the given values of amount, principal amount and simple interest in the simple interest formula.

Complete step-by-step answer:
Given,
The total amount Himanshu paid = Rs. 20,370
The principal amount Himanshu borrowed = Rs. 12,000
The rate of simple interest for the time being = \[15\dfrac{1}{2}%=\left( 15+\dfrac{1}{2} \right)%=15.5%\]
We know that the formula for simple interest is given by A = SI + P
Where A, SI, P represent the amount, simple interest and principal amount respectively.
By substituting the given values in the above formula, we get
20370 = SI + 12000
SI = 20370 – 12000 = Rs. 8370
We know that the formula for simple interest is given by \[\dfrac{PRT}{100}\]
Where R, T represent rate of interest and time period respectively.
By substituting the given and obtained values in the above formula, we get
\[SI=\dfrac{12000\times 15.5\times T}{100}\]
\[\Rightarrow 8370=\left( 120\times 15.5 \right)T\]
\[\Rightarrow 8370=1860T\]
\[\Rightarrow T=\dfrac{8370}{1860}=4.5\]years.
Thus, Himanshu borrowed Rs.12,000 at the rate of simple interest \[15\dfrac{1}{2}%\] for 4.5 years to pay a total sum of Rs. 20,370.

Note: The possibility of mistake can be not using appropriate formula, though the question doesn’t exclusively mention simple interest, it has to be understood since the required parameters to calculate simple interest are given. The alternative way of solving the question is by applying the direct formula for Amount which is given by \[P\left( 1+\dfrac{RT}{100} \right)\] where P, R, T represent principal amount, rate of interest and time period respectively. By substituting the values in the above-mentioned formula, we can calculate the time period.