The average weight of 10 students is increased by half a kg when one of the students weighing 51 kg is replaced by a new student. Find the weight of the new student.

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Step 1: Let the original average weight of 10 students be A kg.

Step 2: Total weight of 10 students = 10 × A.

Step 3: When one student weighing 51 kg is replaced, the average increases by 0.5 kg.

Step 4: New average = A + 0.5.

Step 5: New total weight = 10 × (A + 0.5) = 10A + 5.

Step 6: The increase in total weight = New total weight - Original total weight = (10A + 5) - 10A = 5 kg.

Step 7: This increase is due to replacing the 51 kg student with the new student.

Step 8: Weight of new student = 51 + 5 = 56 kg.

Therefore, the weight of the new student is 56 kg.

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