The following table shows the number of votes polled along with the percentage…
2023
The following table shows the number of votes polled along with the percentage (%) of valid votes and ratio of valid votes of male and females among them during an election in a college for the last five years from 2018-2022. Some values are missing in the table (indicated by '—') that you are expected to calculate if required. Based on the data in the table, answer the questions that follow.
Year-wise Details of Voters Polled in an Election
Year | Number of votes polled | Percentage of valid votes polled (%) | Ratio of valid votes of male and females |
|---|---|---|---|
2018 | — | — | 5:3 |
2019 | 1000 | — | 5:4 |
2020 | 2000 | 38% | — |
2021 | — | 60% | 7:5 |
2022 | 5000 | 40% | — |
In 2018, if the ratio of number of votes to number of valid votes was 5:4, then the number of valid votes by females in 2018 is ____% less than the number of votes polled in the same year.
Answer: D. 70 — ConceptWhen one quantity is a fixed fraction of a reference total, multiply successive fractions to express it as a fraction of that same total. If a quantity…
- A.
60
- B.
30
- C.
35
- D.
70
Attempted by 2 students.
Show answer & explanation
Correct answer: D
Concept
When one quantity is a fixed fraction of a reference total, multiply successive fractions to express it as a fraction of that same total.
If a quantity equals p% of a reference value, then it is (100 − p)% less than that reference value.
Application
Let the number of votes polled in 2018 be V.
The ratio of polled votes to valid votes is 5:4, so valid votes = (4/5)V.
The valid-vote ratio of males to females is 5:3. Therefore, females receive 3/(5 + 3) = 3/8 of the valid votes.
Female valid votes = (3/8) × (4/5)V = (3/10)V = 30% of V.
Hence, the percentage by which female valid votes are less than total polled votes is 100% − 30% = 70%.
Cross-check
If V = 1000, valid votes are 800 and female valid votes are (3/8) × 800 = 300. The shortfall from 1000 is 700, which is 70% of 1000.
Result
The required percentage is 70%.