A lent Rs. 600 to B for 2 years and Rs. 150 to C for 4 years and received altogether from bothRs. 90 as simple interest. The rate of interest is-

Options

A. `4%`
B. `5%`
C. `10%`
D. `12%`

Answer

To solve the problem, we need to calculate the rate of interest using the simple interest formula. Let's break down the solution step by step.

### Step 1: Understand the Simple Interest Formula
The formula for Simple Interest (SI) is given by:
\[ SI = \frac{P \times R \times T}{100} \]
where:
- \(SI\) = Simple Interest
- \(P\) = Principal amount
- \(R\) = Rate of interest per annum
- \(T\) = Time in years

### Step 2: Calculate Simple Interest from B
For B, the principal amount is Rs. 600, the time is 2 years, and we need to find the interest:
\[ SI_B = \frac{600 \times R \times 2}{100} = \frac{1200R}{100} = 12R \]

### Step 3: Calculate Simple Interest from C
For C, the principal amount is Rs. 150, the time is 4 years, and we need to find the interest:
\[ SI_C = \frac{150 \times R \times 4}{100} = \frac{600R}{100} = 6R \]

### Step 4: Total Simple Interest
According to the problem, the total simple interest received from both B and C is Rs. 90:
\[ SI_B + SI_C = 90 \]
Substituting the values we calculated:
\[ 12R + 6R = 90 \]
\[ 18R = 90 \]

### Step 5: Solve for R
Now, we can solve for \(R\):
\[ R = \frac{90}{18} = 5 \]

### Conclusion
The rate of interest is \(5\%\).

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