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?
Show answer & explanation
Correct answer: C
Explanation
The correct answer is Option 3 i.e. 60.
We know that,
Average = Sum of observations/Number of observations
Now,
Average of X, Y, and Z = 52
⇒ (X + Y + Z)/3 = 52
⇒ X + Y + Z = 156.....(i)
Average of X and Y = 48
⇒ (X + Y)/2 = 48
⇒ X + Y = 96 .....(ii)
Average of Y and Z = 60
⇒ (Y + Z)/2 = 60
⇒ Y + Z = 120 ....(iii)
From equations (i) and (ii),
⇒ Z = (X + Y + Z) - (X + Y)
⇒ Z = 156 - 96
⇒ Z = 60
Also from equations (i) and (iii),
⇒ X = (X + Y + Z) - (Y + Z)
⇒ X = 156 - 120
⇒ X = 36
Now,
⇒ X + Z = 60 + 36 = 96
So,
⇒ Y = (X + Y + Z) - (X + Z)
⇒ Y = 156 - 96
⇒ Y = 60
Hence, the value of Y is 60