At some rate of simple interset, A lent Rs 6,000 to B for 2 years and Rs 1,500 to C for 4 years and received Rs 9,00 as interset from both of them together. The rate of interest per annum was

Options

A. 0.05
B. 0.06
C. 0.08
D. 0.1

Answer

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

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

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

### Step 1: Calculate Simple Interest from B
A lent Rs 6,000 to B for 2 years. The Simple Interest earned from B can be calculated as follows:

\[ \text{SI}_B = \frac{6000 \times R \times 2}{100} \]

### Step 2: Calculate Simple Interest from C
A lent Rs 1,500 to C for 4 years. The Simple Interest earned from C can be calculated as follows:

\[ \text{SI}_C = \frac{1500 \times R \times 4}{100} \]

### Step 3: Set up the equation for total interest
According to the problem, the total interest received from both B and C is Rs 900. Therefore, we can write the equation:

\[ \text{SI}_B + \text{SI}_C = 900 \]

Substituting the expressions from Step 1 and Step 2 into the equation:

\[ \frac{6000 \times R \times 2}{100} + \frac{1500 \times R \times 4}{100} = 900 \]

### Step 4: Simplify the equation
Now, we can simplify the equation:

1. Simplifying the first term:
\[ \frac{6000 \times R \times 2}{100} = 120R \]

2. Simplifying the second term:
\[ \frac{1500 \times R \times 4}{100} = 60R \]

Now, substituting back into the equation:

\[ 120R + 60R = 900 \]

Combine like terms:

\[ 180R = 900 \]

### Step 5: Solve for R
Now, we can solve for \( R \):

\[ R = \frac{900}{180} \]

Calculating this gives:

\[ R = 5 \]

### Conclusion
The rate of interest per annum is **5%**.

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