If simple interest on a certain sum of money for 4 years at 5% p.a. is same as the simple interest on Rs. 560 for 10 years at the rate of 4% p.a. then find the sum of money.

Answer

To solve the problem step by step, we will first calculate the simple interest on Rs. 560 for 10 years at the rate of 4% per annum, and then set that equal to the simple interest on the unknown sum of money (let's call it X) for 4 years at 5% per annum.

### Step 1: Calculate the Simple Interest on Rs. 560
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

For Rs. 560 at 4% for 10 years:
- \( P = 560 \)
- \( R = 4 \)
- \( T = 10 \)

Substituting these values into the formula:
\[ SI = \frac{560 \times 4 \times 10}{100} \]

### Step 2: Simplify the Calculation
Calculating the numerator:
\[ 560 \times 4 = 2240 \]
Then, multiply by 10:
\[ 2240 \times 10 = 22400 \]
Now, divide by 100:
\[ SI = \frac{22400}{100} = 224 \]

### Step 3: Set Up the Equation for the Unknown Sum (X)
Now, we know that the simple interest on the sum of money (X) for 4 years at 5% is equal to 224. We can set up the equation:
\[ \frac{X \times 5 \times 4}{100} = 224 \]

### Step 4: Simplify the Equation
Calculating the left side:
\[ \frac{X \times 20}{100} = 224 \]
This simplifies to:
\[ \frac{X}{5} = 224 \]

### Step 5: Solve for X
To find X, multiply both sides by 5:
\[ X = 224 \times 5 \]
Calculating the right side:
\[ X = 1120 \]

### Conclusion
The sum of money is Rs. 1120.

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