Question
In a group, if 3 people with an average weight of 70 kg
leave, the average weight of the remaining group drops by 2 kg. However, if 4 people of average weight 68 kg leave, the average decreases by 2.5 kg. How many people were in the group initially?Solution
ATQ,
Let the number of people in group and average weight be 'n' and 'm' kg, respectively.
So,
mn - 3 × 70 = (n - 3) × (m - 2)
⇒ mn - 210 = mn - 2n - 3m + 6
⇒ 2n + 3m = 216 --------- (I)
And,
mn - 4 × 68 = (n - 4) × (m - 2.5)
⇒ mn - 272 = mn - 2.5n - 4m + 10
⇒ 2.5n + 4m = 282 -------- (II)
Now solving:
Multiply (I) by 4: 8n + 12m = 864
Multiply (II) by 3: 7.5n + 12m = 846
Subtracting:
0.5n = 18
⇒ n = 36
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