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 males 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 2021, if the difference between the number of valid votes polled by males and females was 300, then the number of votes polled in 2021 was
Answer: B. 3000 — CONCEPTWhen a total is divided in the ratio a:b, one ratio part equals the difference between the two shares divided by a−b. The combined share is a+b parts.…
- A.
3690
- B.
3000
- C.
3120
- D.
3440
Show answer & explanation
Correct answer: B
CONCEPT
When a total is divided in the ratio a:b, one ratio part equals the difference between the two shares divided by a−b. The combined share is a+b parts. If a known percentage of a total equals a value, divide that value by the percentage written as a decimal to recover the total.
APPLICATION
The male-to-female valid-vote ratio is 7:5, so the difference represents 7−5=2 parts.
Since 2 parts equal 300 votes, 1 part equals 300÷2=150 votes.
Total valid votes equal (7+5)×150=12×150=1,800.
The 1,800 valid votes are 60% of all votes polled, so total votes polled equal 1,800÷0.60=3,000.
CROSS-CHECK
At 3,000 total votes, 60% gives 1,800 valid votes. Splitting 1,800 in the ratio 7:5 gives 1,050 male votes and 750 female votes, whose difference is 300.
Therefore, the number of votes polled in 2021 was 3,000.