The average weight of 10 men is increased by 1.5Kg when one of the men,who weighs 68kg is replaced by a new man.Find the weight of new man
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82
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83
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81
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80
The total weight increase for 10 men is $10 \times 1.5 = 15$ kg. Since the new man replaced a man weighing 68 kg, his weight must be $68 + 15 = 83$ kg. Options like 82 or 81 do not account for the total weight shift correctly.
To solve this problem, we can use the concept of averages.
Let's assume the initial average weight of the 10 men is represented by "X" kg.
According to the given information, when one of the men weighing 68 kg is replaced by a new man, the average weight increases by 1.5 kg.
We can set up the following equation to represent this situation:
[ \frac{{10X - 68 + W}}{{10}} = X + 1.5 ]
Where:
- ( 10X ) represents the total weight of the 10 men initially
- 68 represents the weight of the man being replaced
- W represents the weight of the new man
- ( X + 1.5 ) represents the new average weight
Now, let's solve this equation to find the weight of the new man:
[ \frac{{10X - 68 + W}}{{10}} = X + 1.5 ]
Multiply both sides of the equation by 10 to eliminate the denominator:
[ 10X - 68 + W = 10X + 15 ]
Subtract 10X from both sides of the equation to isolate W:
[ W - 68 = 15 ]
Add 68 to both sides of the equation to solve for W:
[ W = 15 + 68 ]
[ W = 83 ]
Therefore, the weight of the new man is 83 kg.
The correct answer is option B) 83 kg.