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 -
What is the ratio of candidates qualifying from P in 2017, 2018 and 2020 together to the candidates qualifying from Q in 2017, 2019 and 2020 together?
432 : 205
To find the ratio of candidates qualifying from State P in 2017, 2018, and 2020 together to those qualifying from State Q in 2017, 2019, and 2020 together, we need to calculate the number of qualified candidates for the specified years by using the given percentages of qualified candidates.
- Calculate Qualified Candidates for State P:
- 2017: \(1800 \times \frac{60}{100} = 1080\)
- 2018: \(2400 \times \frac{43}{100} = 1032\)
- 2020: \(1920 \times \frac{70}{100} = 1344\)
- Total qualified candidates from State P for 2017, 2018, and 2020: \(1080 + 1032 + 1344 = 3456\)
- Calculate Qualified Candidates for State Q:
- 2017: \(1520 \times \frac{30}{100} = 456\)
- 2019: \(1040 \times \frac{60}{100} = 624\)
- 2020: \(800 \times \frac{70}{100} = 560\)
- Total qualified candidates from State Q for 2017, 2019, and 2020: \(456 + 624 + 560 = 1640\)
- Finding the Ratio:
- Ratio of P (2017, 2018, 2020) to Q (2017, 2019, 2020) is: \(\frac{3456}{1640}\)
- Simplifying, divide both terms by the greatest common divisor which is 8: \(\frac{3456 \div 8}{1640 \div 8} = \frac{432}{205}\)
Thus, the ratio of candidates qualifying from P in 2017, 2018, and 2020 to those from Q in the years specified is 432 : 205.
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