Question

In a team of four wrestlers, the average weight is increased by 5kg when one of the wrestler weighing 90kgs leaves the team and a new wrestler joins. Find the weight of new wrestler who joined the team.

Answer 1

Since one of the wrestlers weighs 90 kgs; lets have the weights of the other wrestlers as b, c and d. Also, let X be the average weight. Let us also assume the weight of the new person joining in be = z

In first case, we have average weight X = (90 + b + c + d)/4 --------------- (i)

In the second case, we have average weight X + 5 = (z + b + c + d)/4
or
X =  -5 + (z + b + c + d)/4------------------------------------------------------------- (ii)

Equating (i) and (ii), we get the following:
(90 + b + c + d)/4 = -5 + (z + b + c + d)/4

Solving this, we get z = 110kgs.

So the weight of the new wrestler is 110kgs

Answer 2

Number of wrestlers = 4
increase in average weight = 5 kg
increase in sum total of weights of 4 wrestlers = 4 * 5 = 20 kg

so weight of new wrestler - weight of wrestler leaving = 20 kg

Weight of the new wrestler = 90 kg + 20 kg = 110 kg.