In an examination, $15 \%$ of the candidate passed. $24$ of these were girls. The remaining $\frac{3}{5}$ of the candidates who passed were boys. $90$ boys failed the examination. What percentage of the total number of candidates were girls who failed the examination?

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Multiply fractions: word problems

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Q. In an examination,

15 \%

of the candidate passed.

24

of these were girls. The remaining

\frac{3}{5}

of the candidates who passed were boys.

90

boys failed the examination. What percentage of the total number of candidates were girls who failed the examination?

Calculate Total Passed: Calculate the total number of candidates who passed. Since $24$ girls passed and they make up $40\%$ of those who passed (since $60\%$ were boys), we can set up the equation: $\newline$ 24 = 0.4 \times \text{Total_passed} $\newline$ \text{Total_passed} = \frac{24}{0.4} $\newline$ \text{Total_passed} = 60
Calculate Boys Passed: Calculate the total number of boys who passed. Since $60\%$ of those who passed were boys: $\newline$ $\text{Boys\_passed} = 0.6 \times \text{Total\_passed}$ $\newline$ $\text{Boys\_passed} = 0.6 \times 60$ $\newline$ $\text{Boys\_passed} = 36$
Calculate Total Boys: Calculate the total number of candidates. Since $90$ boys failed and $36$ boys passed: $\newline$ $\text{Total\_boys} = \text{Boys\_passed} + \text{Boys\_failed}$ $\newline$ $\text{Total\_boys} = 36 + 90$ $\newline$ $\text{Total\_boys} = 126$
Calculate Total Candidates: Calculate the total number of candidates using the percentage that passed. Since $15\%$ passed: $\newline$ Total\_candidates = Total\_passed / $0$ . $15$ $\newline$ Total\_candidates = $60 / 0.15$ $\newline$ Total\_candidates = $400$
Calculate Girls Failed: Calculate the number of girls who failed. Since the total number of candidates is $400$ and $24$ girls passed: $\newline$ $\text{Girls\_failed} = \text{Total\_candidates} - \text{Total\_boys} - \text{Girls\_passed}$ $\newline$ $\text{Girls\_failed} = 400 - 126 - 24$ $\newline$ $\text{Girls\_failed} = 250$
Calculate Percentage Girls Failed: Calculate the percentage of girls who failed. Since $250$ girls failed out of $400$ total candidates: $\newline$ $\text{Percentage\_girls\_failed} = \left(\frac{\text{Girls\_failed}}{\text{Total\_candidates}}\right) * 100$ $\newline$ $\text{Percentage\_girls\_failed} = \left(\frac{250}{400}\right) * 100$ $\newline$ $\text{Percentage\_girls\_failed} = 62.5\%$