There are 50 boys in a class. One boy weighing 40 kg goes away and at the same time another boy joins the class. If the average weight of the class is thus decreased by 100 g, find the weight of the new boy.

Sure, let's solve this step by step:

Step 1: Calculate the total weight of the boys before the change. The total weight is the average weight times the number of boys. However, we don't know the original average weight. We can express it in terms of the final average weight. Since the average weight decreased by 100g (or 0.1kg) when one boy left and another joined, the original average weight was the final average weight plus 0.1kg. The total weight is therefore (final average weight + 0.1kg) * 50kg.

Step 2: Calculate the total weight after the change. The total weight is still the average weight times the number of boys. The average weight is now the final average weight, so the total weight is (final average weight * 50kg).

Step 3: Set up an equation. The total weight before the change minus the weight of the boy who left is equal to the total weight after the change minus the weight of the boy who joined. We can express this as: (final average weight + 0.1kg) * 50kg - 40kg = final average weight * 50kg - weight of new boy

Step 4: Solve for the weight of the new boy. Rearranging the equation gives us: weight of new boy = (final average weight + 0.1kg) * 50kg - final average weight * 50kg + 40kg Simplifying this gives us: weight of new boy = 0.1kg * 50kg + 40kg = 5kg + 40kg = 45kg

So, the new boy weighs 45kg.