Question 7
SSC-CGL 2018 June 4 Shift 2
The average weight of some students in a class is 68.5 kg. If four new students of 72.2 kg, 70.8 kg, 70.3 kg, 66.7 kg are enrolled in the class, the average weight of students increases by 300 g. Initially, how many students were there in the class?
- 11
- 26
- 21
- 16
Solution 1
simpler method, but needs a deeper understanding of the concept of averagesSuppose four students each of 68.5 kg were already in the group so that the group average of (N + 4) students is 68.5 kg.
The total weight of these four would be 68.5 x 4 = 274 kg.
But the actual weight is (72.3 + 70.8 + 70.3 + 66.7) = 280 kg.
The additional 280 - 274 = 6 kg has increased the group average by 0.3 kg (given 300 gm).
We can say, the weight of 6 kg is distributed as 300 gm to every student of the (N + 4) group.
$\displaystyle \therefore 6 = (N + 4) \times 0.3$
$\displaystyle \implies N = 16$ answer!
Solution 2
Let N be the students with a total weight of N x 68.5
When four students of 280 kg are added, new total weight of the group is N x 68.5 + 280, and the new average is 68.8 kg
$\displaystyle \implies \frac{N \times 68.5 + 280}{N + 4} = 68.8$
Solving for N we get N = 16 answer!
This is a long method, but remember that long methods are standard techniques taught in our NCERT books, and also the world over. It pays to learn them because there is an overall saving in time. Longer methods can be applied to any type of question, even those ones where there is a slight twist.
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