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

Options

A. Rs 700
B. Rs 6500
C. Rs 4000
D. Rs 1500

Answer

To solve the problem step by step, we need to calculate the interest A receives from B and C, and then determine how much A lent to C.

### Step 1: Calculate the interest received from B
A lends Rs 2500 to B at a rate of 7% per annum for 4 years.

The formula for calculating simple interest (SI) is:
\[ SI = \frac{P \times R \times T}{100} \]
Where:
- \(P\) = Principal amount (the sum lent)
- \(R\) = Rate of interest per annum
- \(T\) = Time in years

Substituting the values for B:
- \(P = 2500\)
- \(R = 7\)
- \(T = 4\)

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

### Step 2: Calculate the total interest received from B and C
According to the problem, the total interest received from both B and C after 4 years is Rs 1120.

Let the interest received from C be \(SI_C\). Therefore, we have:
\[ SI_B + SI_C = 1120 \]
Substituting the value of \(SI_B\):
\[ 700 + SI_C = 1120 \]

### Step 3: Solve for the interest from C
Now, we can find \(SI_C\):
\[ SI_C = 1120 - 700 = 420 \]

### Step 4: Calculate the principal amount lent to C
Now we need to find out how much A lent to C. Let the principal amount lent to C be \(P_C\).

Using the simple interest formula again for C:
\[ SI_C = \frac{P_C \times R \times T}{100} \]
Substituting the known values:
\[ 420 = \frac{P_C \times 7 \times 4}{100} \]
\[ 420 = \frac{P_C \times 28}{100} \]

### Step 5: Rearranging to find \(P_C\)
Now, rearranging the equation to solve for \(P_C\):
\[ P_C = \frac{420 \times 100}{28} \]
Calculating \(P_C\):
\[ P_C = \frac{42000}{28} = 1500 \]

### Conclusion
Thus, the sum lent to C is Rs 1500.