In a class of 60 students, the number of girls is twice the number of boys. Laxmi is a girl and she is ranked 27th from the top of the class. If there are exactly 9 boys placed ahead of Laxmi in the merit list, how many girls are ranked after Laxmi in the class?

Introduction / Context:
This question combines ratio information about the composition of a class with ranking information. You must calculate how many girls come after Laxmi by carefully breaking down the total number of girls and how many girls appear before or at her position in the ranking.

Given Data / Assumptions:

• Total number of students in the class = 60.
• Number of girls is twice the number of boys.
• Laxmi is ranked 27th from the top.
• There are 9 boys ahead of Laxmi.
• Laxmi herself is a girl.

Concept / Approach:
We will first find the exact number of boys and girls using the ratio condition. Then we determine how many girls are at or above Laxmi's position. The difference between the total number of girls and the number of girls up to Laxmi gives the number of girls ranked after her.

Step-by-Step Solution:
Step 1: Let the number of boys be B and the number of girls be G. Step 2: We are told that G = 2B and that B + G = 60. Step 3: Substitute: B + 2B = 60 gives 3B = 60, so B = 20. Step 4: Therefore, G = 2B = 40 girls in total. Step 5: Laxmi is 27th from the top. That means there are 26 students ahead of her. Step 6: Out of these 26 students, 9 are boys (given). So the number of girls ahead of Laxmi = 26 - 9 = 17. Step 7: Laxmi herself is also a girl. So the number of girls up to and including Laxmi = 17 + 1 = 18. Step 8: Total number of girls is 40. Therefore, the number of girls ranked after Laxmi = 40 - 18 = 22.
Verification / Alternative check:
We can check consistency by counting total students after Laxmi: there are 60 - 27 = 33 students behind her. Among them, the number of girls is 22, so the number of boys after Laxmi is 33 - 22 = 11. Since there are 20 boys in total and 9 are ahead of Laxmi, 11 boys must indeed be behind her, which matches our calculation.

Why Other Options Are Wrong:
23, 21, 24, 20: These values result from small calculation mistakes such as forgetting to include Laxmi when counting girls up to her rank, using the wrong total number of girls, or subtracting incorrectly when computing how many girls are behind her.
Common Pitfalls:
Typical errors include assuming that Laxmi might be counted among the boys or forgetting to deduct the boys from the students ahead of her to get the correct count of girls. Another mistake is ignoring the total girls computed from the ratio and instead trying to guess how many girls are behind her directly from the ranks, which tends to produce inconsistent numbers.

Final Answer:
The number of girls ranked after Laxmi is 22.