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

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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