Question

A sum of Rs. 8000 amounts to Rs. 10000 in 2 years at simple interest. What is the rate of interest?

• A. 10\%
• B. 12.5\%
• C. 15\%
• D. 20\%

Hint:

Simple interest problems are direct formula applications.

Answer 1

The Correct Option is B

To solve this problem, we need to determine the rate of interest for a sum of Rs. 8000 that amounts to Rs. 10000 in 2 years with simple interest. We will employ the formula for simple interest to find the rate.

The formula for simple interest (SI) is:

\[ SI = \frac{P \times R \times T}{100} \]

Where:

• \(P\) = Principal amount
• \(R\) = Rate of interest per annum
• \(T\) = Time in years
• \(SI\) = Simple interest

First, we calculate the simple interest by finding the difference between the amount and the principal:

\[ SI = 10000 - 8000 = 2000 \]

We know:

• \(P = 8000\)
• \(SI = 2000\)
• \(T = 2\) years

Substitute these values into the simple interest formula to find the rate \(R\):

\[ 2000 = \frac{8000 \times R \times 2}{100} \]

Simplifying the equation for \(R\):

\[ 2000 = \frac{16000R}{100} \]

Rearranging the equation gives:

\[ 200000 = 16000R \]

Dividing both sides by 16000:

\[ R = \frac{200000}{16000} \]

This simplifies to:

\[ R = 12.5\% \]

Thus, the rate of interest is 12.5%.