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The average weight of some children in a group was 48.5 kg. When 6 students having average weight 50.4 kg left the group and 4 students having average weight 56.55 kg joined the group, then the average weight of the children in the group increased by 0.8 kg. The number of children, initially, in the group was

The average weight of some children in a group was 48.5 kg. When 6 students having average weight 50.4 kg left the group and 4 students having average weight 56.55 kg joined the group, then the average weight of the children in the group increased by 0.8 kg. The number of children, initially, in the group was Correct Answer 28

Given:

The average weight of some children in a group was 48.5 kg.

6 students having average weight 50.4 kg left the group.

4 students having average weight 56.55 kg joined the group. 

The average weight of the children in the group increased by 0.8 kg

Formula used:

Average weight = Total weight/Number of people

Calculation:

Let total number of students in the group be x

Average weight of x students = 48.5

Sum of weight of x students = 48.5x

Average weight of 6 students = 50.4

Sum of weight of 6 students = 50.4 × 6 = 302.4

Average weight of 4 students = 56.55

Sum of weight of 4 students = 56.55 × 4 = 226.2

According to the question,

48.5x – 302.4 + 226.2 = (x – 6 + 4) (48.5 + 0.8)

⇒ 48.5x – 76.2 = (x – 2) 49.3

⇒ 48.5x – 76.2 = 49.3x – 98.6

⇒ 49.3x – 48.5x = 98.6 – 76.2

⇒ 0.8x = 22.4

⇒ x = 22.4/0.8

⇒ x = 28

∴ initially 28 children were in the group.

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