David lent Rs 600 to Robin for 2 years and Rs 150 to Martha for 4 years and received altogether from both Rs 90. Find the rate per cent ?

Options

A. a. 3 %
B. b. 5 %
C. c. 7 %
D. d. 9 %

Answer

To solve the problem, we need to find the rate of interest (R) at which David lent money to Robin and Martha. We will use the formula for Simple Interest (SI), which is:

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

Where:
- \( P \) is the principal amount (the initial amount of money)
- \( R \) is the rate of interest per annum
- \( T \) is the time in years

### Step-by-Step Solution:

1. **Identify the amounts lent and the time periods:**
- David lent Rs 600 to Robin for 2 years.
- David lent Rs 150 to Martha for 4 years.

2. **Set up the Simple Interest equations for both loans:**
- For Robin:
\[ \text{SI}_1 = \frac{600 \times R \times 2}{100} = \frac{1200R}{100} = 12R \]
- For Martha:
\[ \text{SI}_2 = \frac{150 \times R \times 4}{100} = \frac{600R}{100} = 6R \]

3. **Add the Simple Interests together:**
- The total interest received from both loans is given as Rs 90:
\[ \text{SI}_1 + \text{SI}_2 = 90 \]
- Substituting the expressions for SI:
\[ 12R + 6R = 90 \]

4. **Combine like terms:**
\[ 18R = 90 \]

5. **Solve for R:**
\[ R = \frac{90}{18} = 5 \]

6. **Conclusion:**
- The rate of interest (R) is 5%.

### Final Answer:
The rate per cent is **5%**.