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% | — |
If the average number of valid votes polled in 2019 and 2022 was 1270 then the number of valid votes polled by females in 2019 was
Answer: D. 240 — ConceptWhen an average of two quantities is known, their combined total equals the average multiplied by 2. For a ratio a:b, the share of the second group is…
- A.
270
- B.
300
- C.
210
- D.
240
Show answer & explanation
Correct answer: D
Concept
When an average of two quantities is known, their combined total equals the average multiplied by 2.
For a ratio a:b, the share of the second group is b/(a+b) of the total.
Application
The number of valid votes in 2022 is 40% of 5000 = 2000.
The combined valid votes in 2019 and 2022 are 1270 × 2 = 2540.
Therefore, valid votes in 2019 = 2540 − 2000 = 540.
In 2019 the male:female ratio is 5:4, so the female share is 4/(5+4) = 4/9.
Female valid votes in 2019 = 540 × 4/9 = 240.
Cross-check
With 240 female votes, male votes are 240 × 5/4 = 300; 300 + 240 = 540, and (540 + 2000)/2 = 1270. Thus the required number is 240.