Averages, weighted average, simple arithmetic mean problems : Ascent - CAT XAT classes, mock cats

Question 4 the day : August 19, 2003
The question for the day is from the topic of Averages. It is a weighted average question and helps understand the basic concepts in averages and weighted average.

Question
When a student weighing 45 kgs left a class, the average weight of the remaining 59 students increased by 200g. What is the average weight of the remaining 59 students?

1. 57
2. 56.8
3. 58.2
4. 52.2

Correct Answer is 57 kgs. Choice (1) is right.

Explanatory Answer

Let the average weight of the 59 students be A.
Therefore, the total weight of the 59 of them will be 59A.

The questions states that when the weight of this student who left is added, the total weight of the class = 59A + 45
When this student is also included, the average weight decreases by 0.2 kgs.
= A - 0.2
=> 59A + 45 = 60A - 12
=> 45 + 12 = 60A - 59A
=> A = 57.

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