A sum of Rs. 36,000 is divided into two parts. A and B such that the simple interest at the rate of `15%` p.a on A and B after two years and four year. Respectively, is equal. The total interest (in Rs.) received from A is :

Options

A. 1800
B. 36000
C. 5400
D. 7200

Answer

To solve the problem step by step, we can follow these instructions:

### Step 1: Understand the Problem
We have a total sum of Rs. 36,000 divided into two parts, A and B. The simple interest on A for 2 years and on B for 4 years at the rate of 15% per annum is equal.

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

### Step 3: Set Up the Equations
For part A:
\[ SI_A = \frac{A \times 15 \times 2}{100} = \frac{30A}{100} = 0.3A \]

For part B:
\[ SI_B = \frac{B \times 15 \times 4}{100} = \frac{60B}{100} = 0.6B \]

Since the interests are equal:
\[ 0.3A = 0.6B \]

### Step 4: Simplify the Equation
Dividing both sides by 0.3 gives:
\[ A = 2B \]

### Step 5: Use the Total Amount
We know that:
\[ A + B = 36,000 \]
Substituting \(A\) from the previous equation:
\[ 2B + B = 36,000 \]
\[ 3B = 36,000 \]

### Step 6: Solve for B
Dividing both sides by 3:
\[ B = \frac{36,000}{3} = 12,000 \]

### Step 7: Solve for A
Using \(A = 2B\):
\[ A = 2 \times 12,000 = 24,000 \]

### Step 8: Calculate the Interest from A
Now we can calculate the simple interest from A:
\[ SI_A = 0.3A = 0.3 \times 24,000 = 7,200 \]

### Final Answer
The total interest received from A is Rs. 7,200.

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