The average weight of X, Y and Z is 35 kg. If the average weight of X and Y is 33 kg and that of Y and Z is 29 kg, then what is the weight (in kg) of Y?

From the problem details, we can write down the equations for total weights:
Total weight of X, Y, and Z:

X+Y+Z=35×3=105 kg— (Equation 1)
Total weight of X and Y:

X+Y=33×2=66 kg— (Equation 2)
Total weight of Y and Z:

Y+Z=29×2=58 kg— (Equation 3)
Now, add Equation 2 and Equation 3:

(X+Y)+(Y+Z)=66+58
X+2Y+Z=124 kg— (Equation 4)
Subtract Equation 1 from Equation 4 to find the weight of Y:

(X+2Y+Z)−(X+Y+Z)=124−105
Y=19 kg