Question:
The average weight of 24 students in a class is 52 kg. If the weight of the teacher is added, the average increases by 1 kg. Find the weight of the teacher.
The average weight of 24 students in a class is 52 kg. If the weight of the teacher is added, the average increases by 1 kg. Find the weight of the teacher.
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Whenever one person is added,
first calculate the old total and the new total.
The difference gives the weight (or marks) of the added person.
Updated On: Jun 8, 2026
- \(76\) kg
- \(77\) kg
- \(75\) kg
- \(53\) kg
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The Correct Option is B
Solution and Explanation
Concept:
Average is defined as
\[
\text{Average}
=
\frac{\text{Total Sum}}{\text{Number of Observations}}.
\]
When a new member is added to a group, the total sum changes and therefore the average changes.
Step 1: Calculate the total weight of the students.
Number of students \[ =24 \] Average weight \[ =52 \text{ kg} \] Therefore, \[ \text{Total weight} = 24\times52 = 1248 \text{ kg}. \]
Step 2: Find the new total weight after adding the teacher.
The average increases by \(1\) kg. Hence new average \[ =53 \text{ kg}. \] Total persons \[ =24+1=25. \] Therefore, \[ \text{New Total Weight} = 25\times53 = 1325 \text{ kg}. \]
Step 3: Calculate the teacher's weight.
\[ \text{Teacher's Weight} = 1325-1248 = 77 \text{ kg}. \] Thus, \[ \boxed{77\text{ kg}} \]
Step 1: Calculate the total weight of the students.
Number of students \[ =24 \] Average weight \[ =52 \text{ kg} \] Therefore, \[ \text{Total weight} = 24\times52 = 1248 \text{ kg}. \]
Step 2: Find the new total weight after adding the teacher.
The average increases by \(1\) kg. Hence new average \[ =53 \text{ kg}. \] Total persons \[ =24+1=25. \] Therefore, \[ \text{New Total Weight} = 25\times53 = 1325 \text{ kg}. \]
Step 3: Calculate the teacher's weight.
\[ \text{Teacher's Weight} = 1325-1248 = 77 \text{ kg}. \] Thus, \[ \boxed{77\text{ kg}} \]
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