In a class of 39 students the ratio of boys and girls is 2 : 1. Radhika ranks 15th among all the students from top and 8th among girls from bottom. How many boys are there below Radhika ?

Options

A. A) 9
B. B) 17
C. C) 11
D. D) 15

Answer

To solve the problem step by step, we will follow these instructions:

### Step 1: Determine the number of boys and girls in the class.
The total number of students in the class is 39, and the ratio of boys to girls is 2:1.

- Let the number of boys be \(2x\) and the number of girls be \(x\).
- According to the ratio, we have:
\[ 2x + x = 39 \]
\[ 3x = 39 \]
\[ x = 13 \]

Thus, the number of boys is:
\[ 2x = 2 \times 13 = 26 \]
And the number of girls is:
\[ x = 13 \]

### Step 2: Analyze Radhika's ranking.
Radhika ranks 15th among all students from the top. This means there are 14 students above her.

### Step 3: Determine the number of girls below Radhika.
Radhika ranks 8th among girls from the bottom. This means there are 7 girls below her.

### Step 4: Calculate the number of girls above Radhika.
Since there are a total of 13 girls in the class:
\[ \text{Number of girls above Radhika} = 13 - 7 = 6 \]

### Step 5: Calculate the number of boys above Radhika.
Since Radhika is 15th overall, the number of students above her is 14. Out of these 14 students, 6 are girls (as calculated in Step 4). Therefore, the number of boys above Radhika is:
\[ \text{Number of boys above Radhika} = 14 - 6 = 8 \]

### Step 6: Calculate the number of boys below Radhika.
The total number of boys in the class is 26. Therefore, the number of boys below Radhika is:
\[ \text{Number of boys below Radhika} = 26 - 8 = 18 \]

### Final Answer:
There are **18 boys below Radhika**.

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