Question

A farmer borrowed Rs. 15000 from a money lender at \[13\% \] per annum simple interest and of 3 years he settled the account after paying Rs. 8000 cash and a motorcycle. Find the value of a motorcycle.

Answer 1

Hint: First, we will calculate the simple interest by using the formula for simple interest. Then, we will get the total amount paid by farmer. Then, we will find the value of the motorcycle by subtracting the cash paid by the farmer from the total amount.

Complete step-by-step answer:
Given that the farmer borrowed Rs. 15000 from a money lender at \[13\% \] per annum simple interest for 3 years.
Therefore, the principal amount is Rs. 15000.
Rate is \[13\% \]
Time is 3 years.
The formula for determining simple interest is
Simple Interest \[ = \dfrac{{P \times R \times T}}{{100}}\]
Putting the values of principle, rate and time in the equation. We get
 \[ \Rightarrow S.I. = \dfrac{{15000 \times 13 \times 3}}{{100}}\]
On simplification we get,
 \[ \Rightarrow S.I. = 5850\]
Total Amount = Principal amount + Simple interest
Putting these values of principal amount and simple interest here, we get the total amount to be paid by the farmer.
 \[ \Rightarrow \] Total amount =15000+5850
On simplification we get,
 \[ \Rightarrow \] Total amount =20850
The total amount for farmers to pay is Rs. 20850.
The farmer pays Rs. 8000 cash and a motorcycle
 \[ \Rightarrow \] 8000+ Motorcycle =20850
Hence, the value of motorcycle is
 \[ \Rightarrow \] Motorcycle =20850-8000
On simplification we get,
 \[ \Rightarrow \] Motorcycle =12850
Therefore, the value of motorcycle is Rs. 12,850.

Note: The simple interest is calculated by using the formula
Simple Interest \[ = \dfrac{{P \times R \times T}}{{100}}\]
Where, P is the principle amount.
R is the rate of interest.
And T is the time period.