Question 64

The average of X, Y and Z is 52. The average of X and Y is 48. The average of Y and Z is 60. What is the value of Y?

Solution

The average of X, Y and Z is 52.

$$\frac{X+Y+Z}{3}\ =\ 52$$

X+Y+Z = 156 Eq.(i)

The average of X and Y is 48.

$$\frac{X+Y}{2}\ =\ 48$$

X+Y = 96 Eq.(ii)
The average of Y and Z is 60.

$$\frac{Y+Z}{2}\ =\ 60$$

Y+Z = 120 Eq.(iii)

Add Eq.(ii) and Eq.(iii).

X+Y+Y+Z = 96+120

X+2Y+Z = 216 Eq.(iv)

Eq.(iv)-Eq.(i).

X+2Y+Z-(X+Y+Z) = 216-156

X+2Y+Z-X-Y-Z = 60

The value of Y = 60

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