Question

The average weight of 5 men is decreased by 3 kg when one of them weights 150 kg replaced by another person. This new person is again replaced by anther person whose weight is 30 kg lower than the person he replaced . What is the overall change in he average dueto this dual change?

• A. 6 Kg
• B. 9 Kg
• C. 12 Kg
• D. 15 Kg

Answer 1

Answer:

B. 9 Kg

Step 1: Calculate the weight of the first new person

• Initially, there are 5 men. When one person (weighing 150 kg) is replaced, the average weight decreases by 3 kg.

• A decrease in average means the incoming person is lighter than the outgoing person.

• The total decrease in weight for the group is the change in average multiplied by the number of men: 3 kg/man × 5 men = 15 kg.

• Therefore, the weight of the first new person is the weight of the outgoing person minus this total decrease: 150 kg - 15 kg = 135 kg.

Step 2: Calculate the weight of the second new person

• The person who just joined (weighing 135 kg) is again replaced by another person.

• This second new person's weight is stated to be 30 kg lower than the person he replaced (who weighed 135 kg).

• So, the weight of the second new person is: 135 kg - 30 kg = 105 kg.

Step 3: Determine the overall change in average

• To find the overall change, we compare the weight of the very first person who left (150 kg) with the weight of the final person who is now in the group (105 kg).

• The net change in the group's total weight due to these dual replacements is the final person's weight minus the initial person's weight: 105 kg - 150 kg = -45 kg.

• A negative value indicates a decrease in total weight.

• Finally, the overall change in the average weight is this net change in total weight divided by the number of men: -45 kg / 5 men = -9 kg.

• This means the average weight of the 5 men has decreased by 9 kg overall.