The average weight of 10 boys is increased by 3 kg if one of them weighing 40 kg is replaced by a new boy. The weight of the new boy is:

70 kg 

Average of 10 boys = $\frac{Sum\; of\; weight}{10}$

Let the weight of 9 of them be $x$,

The 10th boy, who weighs 40 kg is replaced by a new boy.

Original weight average was $\frac{x+40}{10}$

This, increases by 3 when new boy(of weight say, $y$) is added,

⇒ $\frac{x+y}{10}$  = $\frac{x+40}{10}$ + 3

⇒ ($x + y$) = ($x + 40$) + 3 x 10

⇒      $y$     =  70

Thus, the weight of the new boy was 70 kg.