Question

The average weight of 8 men is decreased by 3 kg when one of them whose weight is 56 kg is replaced by a new man. What is the weight of the new man?

• A. 30 kg
• B. 36 kg
• C. 34 kg
• D. 32 kg

Answer 1

Answer:

D. 32 kg

Here's how to solve this problem:

1. Calculate the total initial weight of the 8 men:

• Let the initial average weight of the 8 men be 'A'.

• Total initial weight = 8 * A = 8A

2. Calculate the new average weight:

• The average weight decreased by 3 kg.

• New average weight = A - 3

3. Calculate the total new weight of the 8 men:

• Total new weight = 8 * (A - 3) = 8A - 24

4. Set up an equation using the weights:

• The total new weight is also equal to the total initial weight minus the weight of the old man plus the weight of the new man.

• Let the weight of the new man be 'x'.

• 8A - 24 = 8A - 56 + x

5. Solve for x:

• 8A - 24 = 8A - 56 + x

• Subtract 8A from both sides:

  • -24 = -56 + x

• Add 56 to both sides:

  • -24 + 56 = x

  • 32 = x

Therefore, the weight of the new man is 32 kg.