Raghav lent Rs7,500 to Gopal for three years and Rs5,000 to Sachin for four years on simple interest at the same rate of interest, and received Rs3,570 in all from both as interest. The interest paid by Sachin is:

Options

A. Rs 1,580
B. Rs 1,500
C. Rs 1,680
D. Rs 1,600

Answer

To solve the problem step by step, let's break it down.

### Step 1: Understand the problem
Raghav lent Rs. 7,500 to Gopal for 3 years and Rs. 5,000 to Sachin for 4 years at the same rate of simple interest. The total interest received from both is Rs. 3,570. We need to find the interest paid by Sachin.

### Step 2: Write the formula for simple interest
The formula for simple interest (SI) is:
\[ \text{SI} = \frac{P \times R \times T}{100} \]
where:
- \( P \) = Principal amount
- \( R \) = Rate of interest per annum
- \( T \) = Time in years

### Step 3: Calculate the interest for Gopal
For Gopal:
- Principal \( P_1 = 7500 \)
- Time \( T_1 = 3 \) years

Using the formula:
\[ \text{SI}_1 = \frac{7500 \times R \times 3}{100} \]
This simplifies to:
\[ \text{SI}_1 = \frac{22500R}{100} = 225R \]

### Step 4: Calculate the interest for Sachin
For Sachin:
- Principal \( P_2 = 5000 \)
- Time \( T_2 = 4 \) years

Using the formula:
\[ \text{SI}_2 = \frac{5000 \times R \times 4}{100} \]
This simplifies to:
\[ \text{SI}_2 = \frac{20000R}{100} = 200R \]

### Step 5: Set up the equation for total interest
According to the problem, the total interest received from both Gopal and Sachin is Rs. 3,570:
\[ \text{SI}_1 + \text{SI}_2 = 3570 \]
Substituting the expressions we found:
\[ 225R + 200R = 3570 \]
This simplifies to:
\[ 425R = 3570 \]

### Step 6: Solve for R
To find \( R \):
\[ R = \frac{3570}{425} = 8.4 \]
So, the rate of interest \( R \) is 8.4% per annum.

### Step 7: Calculate the interest paid by Sachin
Now we can find the interest paid by Sachin using the rate we just calculated:
\[ \text{SI}_2 = 200R \]
Substituting \( R = 8.4 \):
\[ \text{SI}_2 = 200 \times 8.4 = 1680 \]

### Final Answer
The interest paid by Sachin is Rs. 1,680.

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