The average weight of 19 students was 25 kg. By the admission of new student is reduced to 24.8 kg. The weight of the new student is :

Question

Accepted Answer

To determine the weight of the new student, we need to use the information provided about the average weights before and after the new student was admitted.

1. **Initial Average Weight Calculation:**
   - The average weight of 19 students is 25 kg.
   - Therefore, the total weight of these 19 students is $19 \times 25 = 475$ kg.

2. **New Average Weight Calculation:**
   - After the admission of the new student, the average weight becomes 24.8 kg for 20 students.
   - Therefore, the total weight of these 20 students is $20 \times 24.8 = 496$ kg.

3. **Weight of the New Student:**
   - The weight of the new student can be found by subtracting the total weight of the original 19 students from the total weight of the 20 students.
   - Weight of the new student = Total weight of 20 students - Total weight of 19 students
   - Weight of the new student = $496 - 475 = 21$ kg

Thus, the weight of the new student is 21 kg, which corresponds to Option 4.

**Explanation for Incorrect Options:**

- **Option 1 (24.8 kg):** This option suggests that the new student's weight is equal to the new average weight, which is not possible because the new average is calculated after including the new student's weight. If the new student weighed 24.8 kg, the average would not have changed from the original 25 kg.

- **Option 2 (20.8 kg):** If the new student weighed 20.8 kg, the total weight of the 20 students would be $475 + 20.8 = 495.8$ kg, leading to an average of $495.8/20 = 24.79$ kg, which does not match the given new average of 24.8 kg.

- **Option 3 (20.6 kg):** Similarly, if the new student weighed 20.6 kg, the total weight would be $475 + 20.6 = 495.6$ kg, resulting in an average of $495.6/20 = 24.78$ kg, which again does not match the given new average of 24.8 kg.

Therefore, the correct answer is Option 4, as it accurately reflects the calculations based on the given averages.