If a certain amount is fully distributed among A, B and C in such a way that A receives `1/2` of the amount, B receives `1/3` of the amount and C receives Rs. 1200, then how much money would A receive ?

Options

A. Rs 4000
B. Rs 1600
C. Rs 3600
D. Rs 1800

Answer

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

### Step 1: Assume the Total Amount
Let the total amount be denoted as \( x \).

**Hint:** Start by defining the total amount as a variable to simplify calculations.

### Step 2: Calculate A's Share
A receives \( \frac{1}{2} \) of the total amount. Therefore, A's share can be calculated as:
\[ \text{A's share} = \frac{x}{2} \]

**Hint:** Use fractions to express the shares of each person based on the total amount.

### Step 3: Calculate Remaining Amount After A's Share
After A's share is taken out, the remaining amount is:
\[ \text{Remaining amount} = x - \frac{x}{2} = \frac{x}{2} \]

**Hint:** Subtract A's share from the total to find out how much is left for B and C.

### Step 4: Calculate B's Share
B receives \( \frac{1}{3} \) of the total amount. Therefore, B's share can be calculated as:
\[ \text{B's share} = \frac{x}{3} \]

**Hint:** Again, express B's share as a fraction of the total amount.

### Step 5: Calculate C's Share
C's share can be calculated by subtracting A's and B's shares from the total amount:
\[ \text{C's share} = x - \left(\frac{x}{2} + \frac{x}{3}\right) \]

To simplify this, we need a common denominator. The least common multiple of 2 and 3 is 6. Therefore:
\[ \text{C's share} = x - \left(\frac{3x}{6} + \frac{2x}{6}\right) = x - \frac{5x}{6} = \frac{x}{6} \]

**Hint:** Use a common denominator to combine fractions easily.

### Step 6: Set C's Share Equal to Rs. 1200
According to the problem, C receives Rs. 1200. Therefore, we can set up the equation:
\[ \frac{x}{6} = 1200 \]

**Hint:** Use the information given in the problem to create an equation.

### Step 7: Solve for x
To find the total amount \( x \), multiply both sides of the equation by 6:
\[ x = 1200 \times 6 = 7200 \]

**Hint:** Isolate the variable to find its value.

### Step 8: Calculate A's Share
Now that we have the total amount, we can find A's share:
\[ \text{A's share} = \frac{x}{2} = \frac{7200}{2} = 3600 \]

**Hint:** Use the value of \( x \) to calculate A's share.

### Final Answer
A receives Rs. 3600.

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