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Question
The number of children in a camp is x and their average weight is 20 kg. If 5 children each weighing 12 kg, join the camp or if 10 children each weighing 21 kg leave the camp, the average weight in both the cases remains the same. The value of x is
Options
18
16
15
14
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Solution
15
Explanation:
Total weight of x children = 20x kg.
When 5 children join, then average weight.
`=((20"x"+5xx12)/("x"+5))` ...............(i)
when 10 children leave, Then average weight.
`=((20"x"-21xx10)/("x"-10))` ...............(ii)
From question, (i) = (ii),
`(20"x"+60)/("x"+5)=(20"x"-210)/("x"-10)`
2 (x − 10)(x + 3) = (2x − 21)(x + 5)
2x2 − 14x − 60 = 2x2 − 11x − 105
3x = 105 − 60
x = 15
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