The average weight of 20 students in aclass is increased by 1.8kg when one of the students, who weights 45kg is replaced by a new student. What is the weight of the new student?

To solve this problem, we need to understand that the average weight of the students increased by 1.8 kg when one student was replaced. This means that the new student must weigh more than the student they replaced.

1. First, we calculate the total increase in weight. Since the average increased by 1.8 kg for 20 students, the total increase is 1.8 kg * 20 = 36 kg.

2. Then, we subtract the weight of the student who left. The total weight increased by 36 kg, but we lost 45 kg when the student left, so the new student must weigh 36 kg + 45 kg = 81 kg.

So, the new student weighs 81 kg.

Sure, let's solve this step by step:

Step 1: The total weight of the 20 students before the new student arrived was 20 * average weight. The average weight was increased by 1.8 kg, so the original average weight was 1.8 kg less.

Step 2: So, the total weight of the 20 students before the new student arrived was 20 * (1.8 kg + original average weight).

Step 3: When the student who weighed 45 kg left, the total weight became 20 * (1.8 kg + original average weight) - 45 kg.

Step 4: The total weight after the new student arrived is 20 * (1.8 kg + original average weight + 1.8 kg), because the average weight increased by 1.8 kg.

Step 5: So, the weight of the new student is 20 * (1.8 kg + original average weight + 1.8 kg) - [20 * (1.8 kg + original average weight) - 45 kg].

Step 6: Simplifying, we find that the weight of the new student is 45 kg + 20 * 1.8 kg = 45 kg + 36 kg = 81 kg.

So, the new student weighs 81 kg.