Correct Option (3):
Initially, the class has 45 students, and the boy's rank from the top is 20th.
- Number of students positioned before him = 19.
- Number of students positioned after him = Total students - His rank = 45 - 20 = 25.
When two additional boys joined the class, the total number of students increased to 45 + 2 = 47.
His rank "dropped by one," which implies his numerical rank from the top increased by one position. Therefore, his new rank from the top is 20 + 1 = 21st.
To determine his new rank from the end of the class:
- Number of students positioned after him in the new arrangement = Total new students - His new rank from the top = 47 - 21 = 26.
- His new rank from the end = (Number of students positioned after him) + 1 = 26 + 1 = 27th.
Incorrect Options:
Options 1, 2, and 4 are incorrect as they result from miscalculations or an incorrect interpretation of the problem statement. Common errors could include:
- Failing to update the total number of students after the two new boys joined.
- Incorrectly interpreting "rank dropped by one" (e.g., assuming his rank improved to 19th, or remained 20th).
- Incorrectly calculating the rank from the end (Rank from end = Total students - Rank from top + 1). For instance, if his rank from the end was calculated based on the initial total students (45) and his initial rank (20th), it would be (45 - 20) + 1 = 26th, which is his initial rank from the end and does not account for the changes.
- Calculating based on 47 students but retaining his original 20th rank would yield (47 - 20) + 1 = 28th (Option 4), which is incorrect because his rank also changed.