Simple interest on Rs. 600 for 4 years at 5.25% per annum is equal to the simple interest on 400 at 5% per annum for a certain period of time. The time period is ?

Options

A. (a) 5 years
B. (b) 20 years
C. (c) 6.3 years
D. (d) 7.2 years

Answer

To solve the problem, we need to find the time period for which the simple interest on Rs. 400 at 5% per annum is equal to the simple interest on Rs. 600 at 5.25% per annum for 4 years.

### Step 1: Calculate the Simple Interest on Rs. 600 for 4 years at 5.25% per annum.

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

Here, \( P = 600 \), \( R = 5.25 \), and \( T = 4 \).

Substituting the values:
\[ SI = \frac{600 \times 5.25 \times 4}{100} \]

### Step 2: Calculate the value.

Calculating the above expression:
\[ SI = \frac{600 \times 5.25 \times 4}{100} = \frac{12600}{100} = 126 \]

So, the simple interest on Rs. 600 for 4 years at 5.25% per annum is Rs. 126.

### Step 3: Set up the equation for the Simple Interest on Rs. 400 at 5% per annum.

Let the time period be \( T \) years. The simple interest on Rs. 400 at 5% per annum is given by:
\[ SI = \frac{P \times R \times T}{100} \]
Where \( P = 400 \) and \( R = 5 \).

So, we have:
\[ SI = \frac{400 \times 5 \times T}{100} \]
This simplifies to:
\[ SI = \frac{2000T}{100} = 20T \]

### Step 4: Set the two simple interests equal to each other.

We know from Step 2 that the simple interest on Rs. 600 is Rs. 126. Therefore:
\[ 20T = 126 \]

### Step 5: Solve for \( T \).

Now, we can solve for \( T \):
\[ T = \frac{126}{20} = 6.3 \]

### Conclusion:

The time period is \( 6.3 \) years.

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