There are some children in a camp and their average weight is 40 kg. If 5 children with average weight 36 kg join the camp or if 5 children with average weight 43.2 kg leave the camp , the average weight of children in both cases is equal. How many children are there in the camp , initially ?
Show answer & explanation
Correct answer: A
Explanation
The correct answer is option 1 i.e. 45
Let total number of children in the camp be x
Average weight of x children = 40
Sum of weight of x children = 40x
Average weight of 5 children = 36
Sum of weight of first 5 children = 36 × 5 = 180
Average weight of second 5 children = 43.2
Sum of weight of 5 children = 43.2 × 5 = 216
(40x + 180)/(x + 5) = (40x - 216)/(x - 5)
(40x + 180)(x - 5) = (40x - 216)(x + 5)
40x2 - 200x + 180x - 900 = 40x2 + 200x - 216x - 1080
4x = 180 = 45