Mohan lens Rs 500 to John and a certain sum to Tom at the same time at a simple interest of 8% per annum. If in 4 years, he altogether Rs. 210 from the two, then the sum of from the two, then the sum of money he lent to Tom was

Options

A. Rs 144.75
B. Rs. 148
C. Rs. 156.25
D. Rs 165.50

Answer

To solve the problem step by step, we will use the formula for simple interest and the information provided in the question.

### Step 1: Identify the known values
- Principal lent to John (P1) = Rs 500
- Rate of interest (R) = 8% per annum
- Time (T) = 4 years
- Total interest received from both John and Tom = Rs 210

### Step 2: Calculate the interest received from John
Using the formula for simple interest:
\[ \text{Simple Interest (SI)} = \frac{P \times R \times T}{100} \]
For John:
\[ SI_1 = \frac{500 \times 8 \times 4}{100} \]
Calculating this:
\[ SI_1 = \frac{500 \times 32}{100} = \frac{16000}{100} = Rs 160 \]

### Step 3: Set up the equation for Tom
Let the principal lent to Tom be Rs \( x \). The interest received from Tom (SI2) can be calculated similarly:
\[ SI_2 = \frac{x \times 8 \times 4}{100} = \frac{32x}{100} = 0.32x \]

### Step 4: Write the equation for total interest
According to the problem, the total interest from both John and Tom is Rs 210:
\[ SI_1 + SI_2 = 210 \]
Substituting the values we calculated:
\[ 160 + 0.32x = 210 \]

### Step 5: Solve for \( x \)
Now, we can solve for \( x \):
\[ 0.32x = 210 - 160 \]
\[ 0.32x = 50 \]
\[ x = \frac{50}{0.32} = 156.25 \]

### Conclusion
The sum of money lent to Tom was Rs 156.25.

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