### CAT Averages

**Question**

Consider a class of 40 students whose
average weight is 40 kgs. m new students join this class whose average weight
is n kgs. If it is known that m + n = 50, what is the maximum possible average
weight of the class now?

- 40.18 kgs
- 40.56 kgs
- 40.67 kgs
- 40.49 kgs

**Correct Answer: Choice (B)**

**Explanation:**

If the overall average
weight has to increase after the new people are added, the average weight of
the new entrants has to be higher than 40.

So, n > 40

Consequently, m has to be
<10 (as n + m = 50)

Working
with the “differences” approach, we know that the total additional weight added
by “m” students would be (n - 40) each, above the already existing average of
40. m(n - 40) is the total extra additional weight added, which is shared
amongst 40+m students. So, m (n – 40)/ (m + 40) has to be maximum for the
overall average to be maximum.

At
this point, use the trial and error approach (or else, go with the answer
options) to arrive at the answer.

The
maximum average occurs when m = 5,and n = 45

And
the average is 40 + (45 – 5) * 5/45 = 40 + 5/9 = 40.56

**Answer Choice (B)**

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