CAT 2017 Quantitative Ability

Question : 28 of 34

Marks: +1, -0

Consider a class of 40 students whose average weight is 40 kg. ‘m’ students join this class and then average weight become V kg. If it is known that m + n = 50, what is the maximum possible average weight of the class now?

40.00
40.56
42.56
41.56

Validate

Solution:

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 exiting 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 m + 40 average to be maximum

At this point, use the trial and error approach to arrive at the answer

The maximum average occurs when m = 5 and n = 45 And the average is

=40+\;\;{5×5}/{45}

{\text "extra weight" × \text "extra number of people"}/{\text "total number of people"}

=40+\;\;{5}/{9}=40.56

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