The following table presents the details about the number of candidates who appeared in an entrance exam and percentage (%) of candidates who qualified the exam from two states P and Q during the years 2017-2021. Some values are missing in the table, and have to be computed, if required. Year-wise Distribution of Candidates in an Entrance ExamYear State P State Q Appeared Qualified Appeared Qualified 2017 1800 60% 1520 30% 2018 2400 43% - 40% 2019 - 60% 1040 60% 2020 1920 70% 800 70% 2021 1520 - 1320 -
In the context of number of qualified candidates from State P in 2019, if the ratio of qualified male to qualified female candidates is 7 : 5 and difference between qualified male and qualified female candidates is 204, then what is the number of candidates who appeared in the exam?
2040
To solve this problem, we need to determine the total number of candidates who appeared for the exam from State P in 2019, given the ratio and difference between qualified male and female candidates.
- We are given the ratio of qualified male to qualified female candidates as 7:5.
- Let the number of qualified male candidates be \(7x\) and qualified female candidates be \(5x\).
- The problem states the difference between the number of qualified male and female candidates is 204:
\(7x - 5x = 204\)
- This simplifies to \(2x = 204\).
- Solving for \(x\) gives \(x = 102\).
- Substitute \(x\) back into the expressions for the number of qualified candidates:
Qualified males: \(7x = 7 \times 102 = 714\)
Qualified females: \(5x = 5 \times 102 = 510\)
- The total number of qualified candidates from State P in 2019 is the sum of qualified males and females:
\(714 + 510 = 1224\)
- According to the table, 60% of the candidates from State P qualified for the exam in 2019.
- Let the total number of candidates who appeared in 2019 be \(A\).
The equation for the number of qualified candidates is: \(0.6 \times A = 1224\)
- Solving for \(A\), we have:
\(A = \frac{1224}{0.6} = 2040\)
- Therefore, the total number of candidates who appeared for the exam from State P in 2019 is 2040.
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