Question

The average weight of three men ‘X’, ‘Y’ and ‘Z’ is 75 kgs. Another man ‘A’ joins the group and the average weight now becomes 80 kgs. If another person ‘B’ whose weight is 5 kgs more than ‘A’ replaces ‘X’, then the average weight of ‘Y’, ‘Z’, ‘A’ and ‘B’ will be 85 kgs. What is the weight of ‘X’?

• A. 78 kgs
• B. 82 kgs
• C. 80 kgs
• D. 84 kgs

Hint:

In average problems involving replacements, set up equations for the total sum of weights before and after the change — subtraction directly gives the unknown.

Answer 1

The Correct Option is C

The average weight of X, Y, and Z is 75 kgs, so: \[ X + Y + Z = 75 \times 3 = 225 \] When A joins, the average becomes 80 kgs for 4 people: \[ X + Y + Z + A = 80 \times 4 = 320 \] From this, \( A = 320 - 225 = 95 \) kgs.
Person B’s weight is 5 kgs more than A: \[ B = 95 + 5 = 100 \ \text{kgs} \] When B replaces X, the group is Y, Z, A, and B, and their average is 85 kgs: \[ Y + Z + A + B = 85 \times 4 = 340 \] Substitute \( A = 95 \) and \( B = 100 \): \[ Y + Z + 95 + 100 = 340 \] \[ Y + Z = 340 - 195 = 145 \] We already know \( X + Y + Z = 225 \), so: \[ X + 145 = 225 \] \[ X = 80 \] Thus, the weight of X is 80 kgs.