The following table shows the number of males (M) and females (F) (in…
2023
The following table shows the number of males (M) and females (F) (in thousands) in Towns X and Y during the five years from 2018 to 2022. Based on the data in the table:
Year wise numbers of Males and Females in two Towns (in thousands)
Year | Town X — number of males | Town X — number of females | Town Y — number of males | Town Y — number of females |
|---|---|---|---|---|
2018 | 50 | 49 | 53 | 50 |
2019 | 52 | 49 | 54 | 52 |
2020 | 55 | 52 | 55 | 54 |
2021 | 53 | 53 | 58 | 56 |
2022 | 55 | 52 | 62 | 55 |
What is the ratio of the average number of males in Town X to the average number of males in Town Y for the given period?
Answer: D. 265:282 — Concept An average is the sum of all observations divided by their count. When two averages use the same number of observations, that common divisor cancels…
- A.
269:282
- B.
265:281
- C.
265:283
- D.
265:282
Show answer & explanation
Correct answer: D
Concept
An average is the sum of all observations divided by their count.
When two averages use the same number of observations, that common divisor cancels in their ratio, so the ratio of the averages equals the ratio of the corresponding sums.
Application
Town X male total = 50 + 52 + 55 + 53 + 55 = 265 thousand.
Town Y male total = 53 + 54 + 55 + 58 + 62 = 282 thousand.
The five-year averages are 265 ÷ 5 = 53 thousand for Town X and 282 ÷ 5 = 56.4 thousand for Town Y.
Therefore, the required ratio is 53 : 56.4. Multiplying both terms by 5 gives 265 : 282. Since 265 and 282 have no common factor greater than 1, this is the simplest form.
Cross-check
As a decimal check, 265 ÷ 282 ≈ 0.9397 and 53 ÷ 56.4 ≈ 0.9397, so the two forms represent the same ratio.
Hence, the ratio of the average male populations is 265 : 282.