There are 48 students in a class. The number of girls is half of the number of boys. If Rashmi is a girl whose rank is 15th from the top and five girls have better ranks than Rashmi, then Rashmi's rank is better than how many boys?
Class Composition Calculation
Let $B$ be the number of boys and $G$ be the number of girls in the class.
- Total students: $B + G = 48$
- Given relation: $G = \frac{1}{2} B$
Substitute the relation into the total students equation:
$B + \frac{1}{2} B = 48$
$ \frac{3}{2} B = 48 $
$ B = 48 \times \frac{2}{3} = 32 $
Number of boys ($B$) = 32.
Number of girls ($G$) = $48 - 32 = 16$.
Analysis of Rashmi's Rank
Rashmi's rank from the top is 15th.
- This means there are $15 - 1 = 14$ students ranked higher than Rashmi.
- Out of these 14 students, 5 are girls.
- Therefore, the number of boys ranked higher than Rashmi is $14 - 5 = 9$.
Rashmi's Rank Relative to Boys
We need to find how many boys have ranks lower (worse) than Rashmi.
- Total number of boys in the class = 32.
- Number of boys ranked higher than Rashmi = 9.
- Number of boys ranked lower than Rashmi = (Total boys) - (Boys ranked higher than Rashmi)
- Number of boys ranked lower than Rashmi = $32 - 9 = 23$.
Rashmi's rank is better than all the boys who are ranked lower than her.
Thus, Rashmi's rank is better than 23 boys.
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