Answer :
To solve this problem, let's break it down step-by-step.
Given:
- The average weight of 29 men increased by 5 kg when one man was replaced.
- The man being replaced weighs 120 kg.
We need to find the weight of the new man.
Step 1: Calculate the original total weight of the 29 men before the replacement.
Let the average weight of the 29 men originally be [tex]x[/tex] kg.
The total weight of the 29 men is [tex]29x[/tex] kg.
Step 2: Calculate the new average weight after the replacement.
The average weight increases by 5 kg, so the new average is [tex]x + 5[/tex] kg.
Step 3: Calculate the new total weight with the new man included.
The total weight for the new average is [tex]29(x + 5)[/tex] kg.
Step 4: Set up the equation and solve for the weight of the new man.
The new total weight also equals the original total minus the weight of the man replaced plus the weight of the new man:
[tex]29(x + 5) = 29x - 120 + \text{weight of the new man}[/tex]
Simplifying gives:
[tex]29x + 145 = 29x - 120 + \text{weight of the new man}[/tex]
Solve for the weight of the new man:
[tex]145 + 120 = \text{weight of the new man}[/tex]
[tex]\text{weight of the new man} = 265 \text{ kg}[/tex]
Thus, the weight of the new man is 265 kg.
Therefore, the correct option is (a) 265.
