Question

The average weight of 8 sailors in a boat is increased by 1 kg if one of them weighing 56 kg is replaced by a new sailor. the weight of the new sailor is

Answer 1

Assume the average weight of 8 sailors = x
Average = Sum total/Number
Sum total = x*8

Now, one weighing 56 kg is replaced by another. Let the weight of new comer be 'y' kg
Sum total = 8*x - 56 + y
Given the average increases by '1', that is 'x+1'
x+1 = 8*x-56+y/8...[Avg = sum total/number]
8*(x+1) = 8x - 56 + y
8*x + 8 = 8x - 56 + y
y = 64
Hence, weight of the new sailor = 64 Kg.
Hope it helps.

Alternatively:
Age of new comer = Replaced weight + (change in avg)*Number of people
                              = 56 + (x-1 - x)*8 = 64 kg