Ram lent Rs 1200 to Shyam for 5 years and Rs 1500 to Mohan for 2 years received altogether Rs 900 as interest. Find the rate per annum.

Options

A. `8.5 %`
B. 0.08
C. 9
D. 10

Answer

To solve the problem step by step, we will use the formula for Simple Interest (SI):

\[ \text{SI} = \frac{P \times R \times T}{100} \]

where:
- \( P \) = Principal amount
- \( R \) = Rate of interest per annum
- \( T \) = Time in years

### Step 1: Calculate the interest for the amount lent to Shyam.

Given:
- Principal (P) = Rs 1200
- Time (T) = 5 years
- Rate (R) = Unknown

Using the formula for Simple Interest:

\[ \text{SI}_{\text{Shyam}} = \frac{1200 \times R \times 5}{100} \]

This simplifies to:

\[ \text{SI}_{\text{Shyam}} = 60R \]

### Step 2: Calculate the interest for the amount lent to Mohan.

Given:
- Principal (P) = Rs 1500
- Time (T) = 2 years
- Rate (R) = Unknown

Using the formula for Simple Interest:

\[ \text{SI}_{\text{Mohan}} = \frac{1500 \times R \times 2}{100} \]

This simplifies to:

\[ \text{SI}_{\text{Mohan}} = 30R \]

### Step 3: Set up the equation for total interest.

According to the problem, the total interest received from both Shyam and Mohan is Rs 900. Therefore, we can write:

\[ \text{SI}_{\text{Shyam}} + \text{SI}_{\text{Mohan}} = 900 \]

Substituting the expressions we found:

\[ 60R + 30R = 900 \]

### Step 4: Combine like terms.

Combining the terms gives:

\[ 90R = 900 \]

### Step 5: Solve for R.

To find the rate \( R \), divide both sides by 90:

\[ R = \frac{900}{90} \]

Calculating this gives:

\[ R = 10 \]

### Conclusion:

The rate of interest per annum is **10%**.

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