Multiple choice

The sum of the ages of X and Y is 45 years, the sum of the ages of Y and Z is 55 years. And the sum of the ages of X and Z is 65 years. What is the age of Y in years?

  1. 17.5

  2. 27.5

  3. 37.5

  4. 19.5

  5. none

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A Correct answer
Explanation

X + Y = 45 (1) Y + Z = 55 (2)
X + Z = 65 (3) (X + Z) – (X + Y) = 65 – 45 [Equation(2) – (1)] = Z – Y = 20 (4) (Z – Y) + (Z + Y) = 20 + 55 [Equation(4) + (2)] = 2Z = 75 = Z = 37.5 Y + 37.5 = 55 (Substituting the value of Z in equation 2) = Y = 17.5