Consider a class of 80 students whose average weight is 80 kg. p new students join the class whose average weight is q kg. If it is known that p + q = 100, find the maximum possible average weight of the class now.?

Option 4 : 80.23 kg

Calculation:

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 80.

∴ q > 80

Consequently, p has to be < 20 (as p + q = 100)

Working with the “difference” approach. We know that the total additional weight added by “q” students would be (q - 80) each, above the already existing average of 80. p (q - 80) is the total extra additional weight added, which is shared amongst 80 + p students.

∴ 80 + (q - 80)/(p + 80) has to be maximum for maximum average.

For p = 1; q = 99 the average is:

⇒ 80 + 19/81

⇒ 80.23 kg

∴ the maximum possible average weight of the class now is 80.23 kg.