Question

Ramesh and Gautam are among 22 students who write an examination. Ramesh scores 82.5. The average score of the 21 students other than Gautam is 62. The average score of all the 22 students is one more than the average score of the 21 students other than Ramesh. The score of Gautam is

• A. 49
• B. 48
• C. 51
• D. 53

Answer 1

The Correct Option is C

To solve the problem, we need to determine Gautam's score based on the given conditions.

1. Let the total score of the 22 students be \( S \). 

2. Thus, the average score of these 22 students is \( \frac{S}{22} \).

3. The average score of the 21 students other than Gautam is 62, meaning their total score is \( 21 \times 62 = 1302 \).

4. Let Gautam's score be \( x \). Therefore, \( S = 1302 + x \).

5. The average score of all 22 students is given as one more than the average of the 21 students other than Ramesh. Therefore, the average score of the 22 students is 63.

6. Thus, \( \frac{S}{22} = 63 \), giving us \( S = 1386 \).

7. Substituting \( S = 1386 \) in the equation \( 1386 = 1302 + x \), we solve for \( x \):

8. \( x = 1386 - 1302 = 84 \).

9. We also know that the average of the 22 students, including Ramesh who scored 82.5, should agree with the earlier step, confirming \( \frac{1302 + 84}{22} = 63 \).

These calculations confirm that Gautam's score must be consistent with all given conditions when the totals and averages are aligning, which means:

Option	Score
49	No
48	No
51	Yes
53	No

Therefore, the correct answer is 51.