Question
A team consists of a certain number of members. If 4
people with an average weight of 65 kg leave the team, the average weight of the remaining members decreases by 1.5 kg. If 5 people each weighing 66 kg leave, the average drops by 2.5 kg. What was the total number of people in the team?Solution
ATQ,
Let the number of team members and average weight be 'n' and 'm' kg, respectively.
So, mn - 4 × 65 = (n - 4) × (m - 1.5)
⇒ mn - 260 = mn - 1.5n - 4m + 6
⇒ 4m + 1.5n = 266 --------- (I)
And, mn - 5 × 66 = (n - 5) × (m - 2.5)
⇒ mn - 330 = mn - 2.5n - 5m + 12.5
⇒ 5m + 2.5n = 342.5 -------- (II)
Now solving:
5 × equation I: 20m + 7.5n = 1330
4 × equation II: 20m + 10n = 1370
Subtracting:
7.5n - 10n = -40
⇒ -2.5n = -40
⇒ n = 16
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