A lends Rs. 2500 to B and a certain sum to C at the same time at 7% per annum,simple interest .If after 4 years, A altogether receives Rs. 1120 as interest from B and C, then find the sum lent to C.

Answer

To solve the problem step by step, we will follow these calculations:

### Step 1: Understand the Problem
A lends Rs. 2500 to B and a certain sum (let's denote it as X) to C at the same time at a rate of 7% per annum as simple interest. After 4 years, the total interest received from both B and C is Rs. 1120. We need to find the sum lent to C (X).

### Step 2: Calculate the Interest from B
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 B:
- \( P = 2500 \)
- \( R = 7 \)
- \( T = 4 \)

Calculating the interest from B:
\[ SI_B = \frac{2500 \times 7 \times 4}{100} = \frac{2500 \times 28}{100} = \frac{70000}{100} = 700 \]

### Step 3: Set Up the Equation for C
Let the sum lent to C be \( X \). The interest from C can be calculated similarly:
\[ SI_C = \frac{X \times 7 \times 4}{100} = \frac{28X}{100} \]

### Step 4: Total Interest Equation
According to the problem, the total interest received from both B and C after 4 years is Rs. 1120:
\[ SI_B + SI_C = 1120 \]
Substituting the values we found:
\[ 700 + \frac{28X}{100} = 1120 \]

### Step 5: Solve for X
Now, we will isolate \( X \):
\[ \frac{28X}{100} = 1120 - 700 \]
\[ \frac{28X}{100} = 420 \]
Multiplying both sides by 100 to eliminate the fraction:
\[ 28X = 42000 \]
Now, divide both sides by 28:
\[ X = \frac{42000}{28} \]
Calculating \( X \):
\[ X = 1500 \]

### Conclusion
The sum lent to C is Rs. 1500.

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