Ram lent Rs. 6,000/- to Shiva for 3 years and Rs. 8,000/- to Krishna for 5 years at the same rate of simple interest per annum. He got a total interest of Rs. 5,220 from both. Find the rate of interest per annum.

Options

A. A)`6%`
B. B)`7%`
C. C)`8%`
D. D)`9%`

Answer

To solve the problem step by step, we will use the formula for simple interest and set up an equation based on the information given.

### Step 1: Understand the Simple Interest Formula
The formula for simple interest (SI) 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 2: Set Up the Equation for Shiva
Ram lent Rs. 6,000 to Shiva for 3 years. Using the simple interest formula, the interest from Shiva can be expressed as:
\[ \text{SI}_{\text{Shiva}} = \frac{6000 \times R \times 3}{100} \]

### Step 3: Set Up the Equation for Krishna
Ram lent Rs. 8,000 to Krishna for 5 years. The interest from Krishna can be expressed as:
\[ \text{SI}_{\text{Krishna}} = \frac{8000 \times R \times 5}{100} \]

### Step 4: Combine the Interests
According to the problem, the total interest from both loans is Rs. 5,220. Therefore, we can set up the equation:
\[ \frac{6000 \times R \times 3}{100} + \frac{8000 \times R \times 5}{100} = 5220 \]

### Step 5: Simplify the Equation
We can simplify the left side:
1. Calculate the interest from Shiva:
\[ \frac{6000 \times R \times 3}{100} = \frac{18000R}{100} = 180R \]
2. Calculate the interest from Krishna:
\[ \frac{8000 \times R \times 5}{100} = \frac{40000R}{100} = 400R \]
3. Combine both:
\[ 180R + 400R = 580R \]

Now, the equation becomes:
\[ 580R = 5220 \]

### Step 6: Solve for R
To find the rate of interest \( R \), divide both sides by 580:
\[ R = \frac{5220}{580} \]

### Step 7: Calculate R
Calculating the value:
\[ R = 9 \]

### Conclusion
The rate of interest per annum is **9%**.