Question

In a class of 60, where boys are twice that of girls, Reena ranked seventeenth from the top. If there are 9 boys ahead of Reena, how many girls are after her in rank?

• A. 13
• B. 12
• C. 31
• D. 21

Hint:

Break rankings by gender counts and include the person in calculation only after separating others before her.

Answer 1

The Correct Option is B

Let \(B\) be the number of boys and \(G\) be the number of girls in the class.

We are given that the total number of students in the class is 60, so

\(B + G = 60\)

We are also given that the number of boys is twice the number of girls, so

\(B = 2G\)

Substituting the second equation into the first equation, we get

\(2G + G = 60\)

\(3G = 60\)

\(G = \frac{60}{3} = 20\)

Thus, the number of girls is 20.

Now, we can find the number of boys:

\(B = 2G = 2(20) = 40\)

So there are 40 boys in the class.

Reena's rank is 17th from the top.

There are 9 boys ahead of Reena.

The remaining students ahead of Reena are girls.

The number of students ahead of Reena is 16 (excluding Reena).

Let \(g\) be the number of girls ahead of Reena. Then

\(g = 16 - 9 = 7\)

So there are 7 girls ahead of Reena.

Since there are 20 girls in the class, the number of girls behind Reena is

\(20 - 1 - 7 = 12\)

However, the number of students ahead of Reena is 16.

Reena's rank is 17th.

The number of students ahead of Reena is 16.

There are 9 boys ahead of Reena.

The number of girls ahead of Reena is \(16 - 9 = 7\).

Reena is a girl.

Total number of girls is 20.

Girls ahead of Reena is 7.

Reena herself is a girl.

Number of girls after Reena = 20 - 7 - 1 = 12.

Therefore, there are 12 girls after her in rank.

Reena is 17th from the top.

There are 9 boys ahead of Reena.

The number of students ahead of Reena is 16.

Number of girls ahead of Reena = 16 - 9 = 7

Total number of girls = 20

The number of girls after Reena = 20 - 7 - 1 = 12

Final Answer: The final answer is \(\boxed{12}\)