The average weight of ten students of class is 40 kg. If the lightest and heaviest student are not taken into account then average weight of remaining students in 41 kg. If the weight of heaviest student is 50 kg, find the weight of lightest student. (in kg)

Options

A. 21
B. 22
C. 23
D. 24

Answer

To solve the problem step by step, let's break it down:

### Step 1: Calculate the total weight of the 10 students.
The average weight of the 10 students is given as 40 kg. The formula for average is:

\[ \text{Average} = \frac{\text{Total Weight}}{\text{Number of Students}} \]

From this, we can rearrange the formula to find the total weight:

\[ \text{Total Weight} = \text{Average} \times \text{Number of Students} \]

Substituting the values:

\[ \text{Total Weight} = 40 \, \text{kg} \times 10 = 400 \, \text{kg} \]

### Step 2: Calculate the total weight of the remaining 8 students.
When the lightest and heaviest students are not included, the average weight of the remaining 8 students is 41 kg. Again, we use the average formula:

\[ \text{Total Weight of 8 Students} = \text{Average} \times \text{Number of Students} \]

Substituting the values:

\[ \text{Total Weight of 8 Students} = 41 \, \text{kg} \times 8 = 328 \, \text{kg} \]

### Step 3: Find the total weight of the lightest and heaviest students.
To find the combined weight of the lightest and heaviest students, we subtract the total weight of the 8 students from the total weight of all 10 students:

\[ \text{Weight of Lightest + Heaviest} = \text{Total Weight} - \text{Total Weight of 8 Students} \]

Substituting the values:

\[ \text{Weight of Lightest + Heaviest} = 400 \, \text{kg} - 328 \, \text{kg} = 72 \, \text{kg} \]

### Step 4: Use the weight of the heaviest student to find the weight of the lightest student.
We know the weight of the heaviest student is 50 kg. We can now find the weight of the lightest student by rearranging the equation:

\[ \text{Weight of Lightest} = \text{Weight of Lightest + Heaviest} - \text{Weight of Heaviest} \]

Substituting the values:

\[ \text{Weight of Lightest} = 72 \, \text{kg} - 50 \, \text{kg} = 22 \, \text{kg} \]

### Conclusion
The weight of the lightest student is **22 kg**.

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