The average weight of A,B and C is x kg, A and C lose y kg each after dieting and B puts on `y/2` kg. Aftre this, average weight decreases by 1 kg. find y.

Options

A. `1.5 kg`
B. 3 kg
C. 2 kg
D. `3.5 kg`

Answer

To solve the problem step by step, we will follow the reasoning laid out in the video transcript.

### Step 1: Understand the Average Weight
The average weight of A, B, and C is given as \( x \) kg. Therefore, the total weight of A, B, and C can be calculated as:
\[ \text{Total weight} = 3 \times x = 3x \text{ kg} \]

**Hint:** Remember that the average is calculated by dividing the total weight by the number of individuals.

### Step 2: Determine Weight Changes
After dieting, A and C lose \( y \) kg each, and B gains \( \frac{y}{2} \) kg. Therefore, the new weights will be:
- A's new weight = \( A - y \)
- B's new weight = \( B + \frac{y}{2} \)
- C's new weight = \( C - y \)

The total weight after these changes will be:
\[ \text{New total weight} = (A - y) + (B + \frac{y}{2}) + (C - y) = (A + B + C) - 2y + \frac{y}{2} \]

**Hint:** Make sure to account for both the losses and gains in weight correctly.

### Step 3: Simplify the New Total Weight
Using the total weight from Step 1, we can substitute:
\[ \text{New total weight} = 3x - 2y + \frac{y}{2} \]
To combine the terms, we can express \( -2y \) as \( -\frac{4y}{2} \):
\[ \text{New total weight} = 3x - \frac{4y}{2} + \frac{y}{2} = 3x - \frac{3y}{2} \]

**Hint:** When combining fractions, ensure they have a common denominator.

### Step 4: Set Up the Equation for the New Average
According to the problem, the new average weight decreases by 1 kg. Therefore, the new average weight is:
\[ \text{New average weight} = x - 1 \]
The total weight for the new average can also be expressed as:
\[ \text{New average} = \frac{\text{New total weight}}{3} = \frac{3x - \frac{3y}{2}}{3} \]
This simplifies to:
\[ \frac{3x - \frac{3y}{2}}{3} = x - 1 \]

**Hint:** Remember that the average is the total weight divided by the number of individuals.

### Step 5: Solve the Equation
Now we can set the two expressions for the new average equal to each other:
\[ x - 1 = x - \frac{y}{2} \]
To eliminate \( x \) from both sides, we simplify:
\[ -1 = -\frac{y}{2} \]
Multiplying both sides by -2 gives:
\[ y = 2 \]

**Hint:** Be careful with signs when solving equations.

### Final Answer
Thus, the value of \( y \) is:
\[ \boxed{2 \text{ kg}} \]