The average weight of X, Y and Z Is 74 kg. If the average weight of X and Y be 68 kg. and that of Y and Z be 78 kg., then the weight (In kg.) of Y is ______

Options

A. 70
B. 68
C. 68
D. 66

Answer

To find the weight of Y, we can follow these steps:

### Step 1: Calculate the total weight of X, Y, and Z.
The average weight of X, Y, and Z is given as 74 kg. Since the average is calculated as the total weight divided by the number of individuals, we can set up the equation:

\[ \text{Average} = \frac{\text{Total Weight}}{\text{Number of Individuals}} \]

Here, the total weight of X, Y, and Z can be calculated as follows:

\[ \frac{X + Y + Z}{3} = 74 \]

Multiplying both sides by 3 gives:

\[ X + Y + Z = 74 \times 3 = 222 \quad \text{(Equation 1)} \]

### Step 2: Calculate the total weight of Y and Z.
The average weight of Y and Z is given as 78 kg. Thus, we can write:

\[ \frac{Y + Z}{2} = 78 \]

Multiplying both sides by 2 gives:

\[ Y + Z = 78 \times 2 = 156 \quad \text{(Equation 2)} \]

### Step 3: Calculate the weight of X.
Now, we can substitute Equation 2 into Equation 1 to find the weight of X:

\[ X + (Y + Z) = 222 \]

Substituting \(Y + Z = 156\) from Equation 2:

\[ X + 156 = 222 \]

Now, solving for X:

\[ X = 222 - 156 = 66 \quad \text{(Weight of X)} \]

### Step 4: Calculate the total weight of X and Y.
The average weight of X and Y is given as 68 kg. Thus, we can write:

\[ \frac{X + Y}{2} = 68 \]

Multiplying both sides by 2 gives:

\[ X + Y = 68 \times 2 = 136 \quad \text{(Equation 3)} \]

### Step 5: Substitute the weight of X to find Y.
Now, we can substitute the value of X into Equation 3:

\[ 66 + Y = 136 \]

Now, solving for Y:

\[ Y = 136 - 66 = 70 \quad \text{(Weight of Y)} \]

### Conclusion
The weight of Y is **70 kg**.

---