Question

A sum fetched a total simple interest of Rs.4016.25 at the rate of 9% p.a. in 5 years. What is the sum?
(a) Rs.4462.50
(b) Rs.8032.50
(c) Rs.8900
(d) Rs.8925

Answer 1

Hint: To solve this question we will use the formula to calculate simple interest SI having principal P, Rate of interest R, and Time T, which is given as,
\[SI=\dfrac{PRT}{100}\]
We have been given the SI, R, and T in the question so substituting them in the above formula will give us the principal amount P or sum directly.

Complete step-by-step solution:
Given that simple interest SI = Rs.4016.25.
Rate of interest R = 9% p.a.
And Time T = 5 years.
Now we will use simple interest formula having principal P, Rate of interest R, and Time T, which is given as,
\[SI=\dfrac{PRT}{100}\]
We have to find the value of the sum which is nothing but the principal amount P.
Substituting, SI = 4016.25, R = 9% and T = 5 years in above formula we get,
\[\begin{align}
  & SI=\dfrac{P\times R\times T}{100} \\
 & \Rightarrow 4016.25=\dfrac{P\times 9\times 5}{100} \\
\end{align}\]
Multiply both sides by 100.
\[\begin{align}
  & \Rightarrow 4016.25\times 100=P\times 45 \\
 & \Rightarrow 45P=401625 \\
\end{align}\]
Dividing both sides by 45 we get,
\[\begin{align}
  & P=\dfrac{401625}{45} \\
 & \Rightarrow P=8925 \\
\end{align}\]
So, the principal amount P that is sum is Rs.8925 which is option (d).

Note: The student should be cautious while considering the rate of interest R. Here rate is given to be 9% per annum (p.a.). So we do not have to count anything. Otherwise if in the question the rate is given per month then we will convert it to per annum and then use it. Because the formula, \[SI=\dfrac{PRT}{100}\] is for per annum only.