The sum required to earn a monthly interest of Rs. 400 at 10% per annum at simple Interest Is
(a) Rs. 45000
(b) Rs. 48000
(c) Rs. 56000
(d) Rs. 40000

Options

A. Rs. 45000
B. Rs. 48000
C. Rs. 56000
D. Rs. 40000

Answer

To solve the problem of finding the principal amount required to earn a monthly interest of Rs. 400 at a rate of 10% per annum using simple interest, we can follow these steps:

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

### Step 2: Identify the Given Values
From the problem, we have:
- Monthly interest (\(SI\)) = Rs. 400
- Rate of interest (\(R\)) = 10% per annum
- Time (\(N\)) = 1 month = \(\frac{1}{12}\) years

### Step 3: Substitute the Known Values into the Formula
Substituting the known values into the simple interest formula:
\[ 400 = \frac{P \times 10 \times \frac{1}{12}}{100} \]

### Step 4: Simplify the Equation
To simplify, we can first multiply both sides by 100 to eliminate the fraction:
\[ 400 \times 100 = P \times 10 \times \frac{1}{12} \]
\[ 40000 = P \times \frac{10}{12} \]

### Step 5: Solve for Principal \(P\)
Now, we can isolate \(P\):
\[ P = \frac{40000 \times 12}{10} \]
\[ P = \frac{480000}{10} \]
\[ P = 48000 \]

### Conclusion
The principal amount required to earn a monthly interest of Rs. 400 at 10% per annum is Rs. 48,000.

### Final Answer
(b) Rs. 48000