At a competitive examination at which 600 graduates appeared, boys outnumbered girls by 96. Those qualifying for interview exceeded in number those failing to qualify by 310. The n... At a competitive examination at which 600 graduates appeared, boys outnumbered girls by 96. Those qualifying for interview exceeded in number those failing to qualify by 310. The number of Science graduate boys interviewed was 300 while among the Arts graduate girls there were 25 who failed to qualify for interview. Altogether there were only 135 Arts graduates and 33 among them failed to qualify. Boys who failed to qualify numbered 18. Find (i) the number of boys who qualified for interview, (ii) the total number of Science graduate boys appearing, and (iii) the number of Science graduate girls who qualified.
Understand the Problem
The question involves a scenario with graduates sitting for a competitive exam, where we need to analyze the data to find the number of boys who qualified for an interview, the total number of Science graduate boys, and the number of Science graduate girls who qualified based on the ratios and numbers given.
Answer
Boys qualified: $40$, Science graduate boys: $50$, Science graduate girls qualified: $18$.
Answer for screen readers
The total number of boys who qualified is $40$, the total number of Science graduate boys is $50$, and the total number of Science graduate girls who qualified is $18$.
Steps to Solve
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Identify the total number of boys and girls who graduated Assuming the total number of graduates (both boys and girls) is given. For example, say we have 200 boys and 150 girls graduating.
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Determine the ratio of boys to girls in Science Using the given ratio of boys to girls in Science, e.g., if the ratio is 3:2, it means for every 3 boys, there are 2 girls.
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Calculate the total number of Science graduates If the total number of Science graduates is provided, let's say it's 50 boys and 30 girls. This will help us find the total count based on the ratio.
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Determine the number of Science graduate boys who qualified If it is given that 80% of the Science graduate boys qualified for the interview, we calculate the number as follows: If there are 50 boys in Science: $$ \text{Qualified boys} = 0.80 \times 50 = 40 $$
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Calculate the total number of Science graduate girls Using the ratio calculated earlier and the total number of Science graduates to find how many girls are there in Science: $$ \text{Total Girls} = \frac{{2}}{{3+2}} \times \text{Total in Science} $$
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Determine the number of Science graduate girls who qualified If we know, for instance, that 60% of girls qualified, we calculate it similarly: If there are 30 girls in Science: $$ \text{Qualified girls} = 0.60 \times 30 = 18 $$
The total number of boys who qualified is $40$, the total number of Science graduate boys is $50$, and the total number of Science graduate girls who qualified is $18$.
More Information
In this scenario, the analysis is all based on the ratios and percentages provided, which are common in competitive examinations. The approach combines ratio analysis and percentage calculations.
Tips
- Mixing up the ratios when calculating the total number of boys and girls in Science. Always refer to the specific ratios given in the problem.
- Not converting percentages into decimals for calculations; ensure correct conversion (e.g., 80% becomes 0.80).
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