averages topic

Question

the average weight of 20 students in a class is decreased by 500g ,when one of the boys whose weight is 45 kg is replaced by a new boy then weight of the new boy is?

Answer 1

Let x = total weight of the students before replacement and let y = average weight of students before replacement. Call the new boy's weight n. Remember that 500 g = 0.5 kg. Then:

 

x/20 = y        (average weight before replacement)

x = 20y

 

(x - 45 + n)/20 = y - 0.5        (total weight with replacement divided by 20 is 500 g less)

20y - 45 + n = 20y - 10        (substitute in x = 20y)

-45 + n = -10

n = 35

 

The new boy weighed 35 kg.