Five athletes are weighed consecutively, and after each measurement, their average weight is calculated. If the average weight increases by 1.5 kg each time, then how much heavier is the last player than the first player?
Show answer & explanation
Correct answer: A
Explanation
The correct answer is option 1 i.e 12 kg.
Let the first athlete's weight = W1
Since the average increases by 1.5 kg each time:
After 1st: average = W1
After 2nd: average = W1 + 1.5
After 3rd: average = W1 + 3
After 4th: average = W1 + 4.5
After 5th: average = W1 + 6
The weights
2nd athlete: W2 = 2 × (W1 + 1.5) − W1 = W1 + 3
3rd athlete: W3 = 3 × (W1 + 3) − (W1 + W2) = W1 + 6
4th athlete: W4 = 4 × (W1 + 4.5) − (W1 + W2 + W3) = W1 + 9
5th athlete: W5 = 5 × (W1 + 6) − (W1 + W2 + W3 + W4) = W1 + 12
Difference between last and first = W5 − W1 = 12 kg