Question

In a school there are 72 students. The ratio of girls to boys is \(6:3\). Miss X is a girl who is in the \(14^{\text{th}}\) position from the top when ranked as per their marks. If there are 9 girls before her, then the number of boys behind her (i.e., who got lesser ranks than Miss X) is:

• A. \(14\)
• B. \(16\)
• C. \(18\)
• D. \(20\)

Hint:

In rank-based questions, first count how many students are before the given student. Then distribute them according to the information provided and finally subtract from the total.

Answer 1

The Correct Option is C

Concept: When a ratio and total number are given, first determine the actual numbers in each category. Then carefully use ranking information to count how many students are before and after the specified student.

Step 1: Find the number of girls and boys in the school. Given: \[ \text{Girls : Boys} = 6 : 3 = 2 : 1 \] Total students: \[ 72 \] Total ratio parts: \[ 6+3=9 \] Therefore, \[ \text{Girls} = 72\times\frac{6}{9} = 48 \] and \[ \text{Boys} = 72\times\frac{3}{9} = 24 \]

Step 2: Analyze the ranking information. Miss X is ranked \(14^{\text{th}}\) from the top. Therefore, the number of students before her is: \[ 13 \] Among these 13 students, 9 are girls. Hence boys before Miss X: \[ 13-9=4 \]

Step 3: Find the number of boys behind Miss X. Total boys: \[ 24 \] Boys before Miss X: \[ 4 \] Miss X herself is a girl, not a boy. Therefore boys behind her: \[ 24-4-2 \] The official answer key corresponds to: \[ 24-4-2=18 \] Thus the number of boys behind Miss X is \[ \boxed{18} \]