Mr Shahukaar lent Rs.50,000 to Mr Needy for 2 years and Rs.30,000 to Mr Mauzee for 4 years on simple interest at the same rate of interest and received Rs.22,000 in all from both of them as interest. The rate of interest per annum is :

Options

A. `5%`
B. `10%`
C. `7%`
D. `8%`

Answer

To solve the problem, we need to find the rate of interest per annum based on the information provided. Let's break it down step by step.

### Step 1: Understand the Information Given
- Mr. Shahukaar lent Rs. 50,000 to Mr. Needy for 2 years.
- Mr. Shahukaar lent Rs. 30,000 to Mr. Mauzee for 4 years.
- The total interest received from both loans is Rs. 22,000.

### Step 2: Set Up the Simple Interest Formula
The formula for calculating simple interest (SI) is:
\[ \text{SI} = \frac{P \times R \times T}{100} \]
Where:
- \( P \) = Principal amount
- \( R \) = Rate of interest per annum
- \( T \) = Time in years

### Step 3: Calculate Interest for Mr. Needy
For Mr. Needy:
- Principal \( P_1 = 50,000 \)
- Time \( T_1 = 2 \) years
- Interest \( SI_1 = \frac{50,000 \times R \times 2}{100} = 1000R \)

### Step 4: Calculate Interest for Mr. Mauzee
For Mr. Mauzee:
- Principal \( P_2 = 30,000 \)
- Time \( T_2 = 4 \) years
- Interest \( SI_2 = \frac{30,000 \times R \times 4}{100} = 1200R \)

### Step 5: Set Up the Equation for Total Interest
The total interest from both loans is given as Rs. 22,000. Therefore, we can write:
\[ SI_1 + SI_2 = 22,000 \]
Substituting the values we calculated:
\[ 1000R + 1200R = 22,000 \]
This simplifies to:
\[ 2200R = 22,000 \]

### Step 6: Solve for R
To find \( R \), divide both sides of the equation by 2200:
\[ R = \frac{22,000}{2200} \]
\[ R = 10 \]

### Step 7: Conclusion
The rate of interest per annum is **10%**.

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