Question:
The average weight of a group of people increases by 2 kg when a person weighing 65 kg joins them. If the initial average weight of the group was 55 kg, find the ratio of the number of people initially in the group to the total number of people in the new group.
The average weight of a group of people increases by 2 kg when a person weighing 65 kg joins them. If the initial average weight of the group was 55 kg, find the ratio of the number of people initially in the group to the total number of people in the new group.
Updated On: Sep 17, 2024
- 5:6
- 4:5
- 3:4
- 2:3
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The Correct Option is B
Solution and Explanation
Let the initial number of people as 'x'
The total initial weight as 'W'
Initial average weight = 55 kg
New person's weight = 65 kg
Increase in average weight = 2 kg
\(\frac{W}{x} = 55\) (Initial average weight) —>eq1
\(\frac{W + 65}{x + 1} = 57\) (New average weight)---> eq2
From eq 1, W = 55x
Substituting W in eq2:
\(\frac{55x + 65}{x + 1} = 57\)
=> 55x + 65 = 57x + 57
=> 2x = 8
=> x = 4
So, the initial number of people (x) is 4.
Total number of people in the new group = x + 1 = 4 + 1 = 5
Therefore, the ratio of the number of people initially in the group to the total number of people in the new group is 4:5.
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