In a class of 5 students, average weight of the 4 lightest students is 40 kgs, Average weight of
the 4 heaviest students is 45 kgs. What is the difference between the the maximum and
minimum possible average weight overall?
(1) 2.8 kgs (2) 3.2 kgs (3) 3 kgs (4) 4 kgs

Hi
Let the five weights be a,b,c,d and e
4 lightest be a,b,c and d
Now (a+b+c+d)/4=40
So a+b+c+d=160 (1)
4 heaviest be b,c,d,e
Now b+c+d+e=180 (2)
subtracting (2) and (1)
we get e-a=20
Now e=20+a
We can say minimum of e is 45
Therefore minimum of a will be 25Kg
so weights becomes 25,45,45,45 and 45 .
Now maximum value of a can be 40Kg
so maximum value of e will be 20+40=60kg
so weights becomes 40,40,40,40 and 60 Kg
Therefore difference in maximum and minimum possible = 220/5 -205/5 = 3kg

3.