A person deposited Rs 400 for 2 years, Rs 550 for 4 years and Rs 1,2000 for 6 years. He received the total simple interset of Rs 1,020. The rate of interset per annum is

Options

A. 0.1
B. 0.05
C. 0.15
D. 0.2

Answer

To find the rate of simple interest per annum, we can use the formula for simple interest:

\[ \text{Simple Interest (SI)} = \frac{P \times R \times T}{100} \]

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

### Step 1: Calculate the Simple Interest for each deposit

1. **For Rs. 400 deposited for 2 years:**
\[ SI_1 = \frac{400 \times R \times 2}{100} = \frac{800R}{100} = 8R \]

2. **For Rs. 550 deposited for 4 years:**
\[ SI_2 = \frac{550 \times R \times 4}{100} = \frac{2200R}{100} = 22R \]

3. **For Rs. 12,000 deposited for 6 years:**
\[ SI_3 = \frac{12000 \times R \times 6}{100} = \frac{72000R}{100} = 720R \]

### Step 2: Set up the equation for total Simple Interest

The total simple interest received is Rs. 1,020. Therefore, we can write the equation:

\[ SI_1 + SI_2 + SI_3 = 1020 \]

Substituting the values we calculated:

\[ 8R + 22R + 720R = 1020 \]

### Step 3: Combine like terms

Combine the terms on the left side:

\[ 750R = 1020 \]

### Step 4: Solve for R

To find the rate \( R \), divide both sides by 750:

\[ R = \frac{1020}{750} \]

Calculating this gives:

\[ R = \frac{34}{25} = 1.36 \]

### Conclusion

The rate of interest per annum is:

\[ R = 1.36\% \]

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