In what time would 5400 at 8% per annum yield the same interest as 2400 at 9% per annum in 4 years ?

Options

A. 2
B. 4
C. 6
D. 8

Answer

To solve the problem, we need to find the time (T) it would take for an investment of ₹5400 at an interest rate of 8% per annum to yield the same interest as an investment of ₹2400 at an interest rate of 9% per annum over 4 years.

### Step-by-Step Solution:

1. **Identify the Interest Formula**:
The formula for calculating simple interest is:
\[ \text{Interest} = \frac{P \times R \times T}{100} \]
where \( P \) is the principal amount, \( R \) is the rate of interest, and \( T \) is the time in years.

2. **Calculate Interest for the Second Investment**:
For the second investment of ₹2400 at 9% for 4 years:
\[ \text{Interest} = \frac{2400 \times 9 \times 4}{100} \]
Simplifying this:
\[ \text{Interest} = \frac{2400 \times 36}{100} = \frac{86400}{100} = 864 \]

3. **Set Up the Equation for the First Investment**:
Now, we want the interest from the first investment (₹5400 at 8% for T years) to equal ₹864:
\[ \frac{5400 \times 8 \times T}{100} = 864 \]

4. **Simplify the Equation**:
Multiply both sides by 100 to eliminate the fraction:
\[ 5400 \times 8 \times T = 86400 \]

5. **Calculate \( 5400 \times 8 \)**:
\[ 5400 \times 8 = 43200 \]
Now the equation becomes:
\[ 43200 \times T = 86400 \]

6. **Solve for T**:
Divide both sides by 43200:
\[ T = \frac{86400}{43200} = 2 \]

Thus, the time required for ₹5400 at 8% per annum to yield the same interest as ₹2400 at 9% per annum in 4 years is **2 years**.