The average weight of some children in a group was 42 kg. When 5 children of average weight 48 kg join the group of 5 children of average weight 37 kg leave the group, the average weight of children in both cases remains equal. How many children were there in the group initially?
Show answer & explanation
Correct answer: D
Explanation
The correct answer is Option 4 i.e. 55.
Let the original number of children = x
The average weight of 5 children with an average weight of 48 kg joins the group
⇒ (42 × x + 5 × 48)/(x + 5)
The average weight of 5 children with an average weight of 37 kg leaves the group
⇒ (42 × x - 5 × 37)/(x - 5)
According to the question,
⇒ (42 × x + 5 × 48)/(x + 5) = (42 × x - 5 × 37)/(x - 5)
⇒ (42x + 240)/(x + 5) = (42x - 185)/(x - 5)
⇒ (x - 5)(42x + 240) = (x + 5)(42x - 185)
⇒ 42x2 + 240x - 210x - 1200 = 42x2 - 185x + 210x - 925
⇒ 30x - 1200 = 25x - 925
⇒ 5x = 275
⇒ x = 55