In a class of 150 students, the number of girls is two-thirds the number of boys. Gowri is ranked 60th from the top, and there ar…

Question

In a class of 150 students, the number of girls is two-thirds the number of boys. Gowri is ranked 60th from the top, and there are 20 girls ahead of her in rank.

How many boys are ranked below Gowri?

1. A. 60
2. B. 39
3. C. 51 (Correct answer)
4. D. 59

Correct Answer

Option C — 51

Detailed Solution & Explanation

The correct answer is 51.

Key Points

• Let the number of boys be b. Girls = (2/3)b, and b + (2/3)b = 150 → (5/3)b = 150 → b = 90 boys and 60 girls.
• Gowri is 60th from the top, so 59 students rank above her.
• Of those 59, 20 are girls, so 59 − 20 = 39 are boys.
• Boys ranked below Gowri = 90 − 39 = 51.

Additional Information

• Gowri is herself a girl, so she is not counted among the boys — which is why the 90 boys split into 39 above her and 51 below, with none tied at her rank.
• The distractor 39 is the count of boys above her, and 59 is the number of students above her; read the direction of the question carefully.

*Ministry of Papers worked solution. The Commission has not yet published the official key for this paper; this answer will be reconciled with it on release.*