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, answer the questions 1-5

Year wise numbers of Males and Females in two Towns (in thousands)

Table X			Table Y
Year	Number of Males	Number of Females	Number of Males	Number of Females
2018	50	49	53	53
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?

The correct answer is 265:282.

To find the ratio of the average number of males in Town X to the average number of males in Town Y, we first need to sum up the male populations for each town across all five years (2018–2022), and then form the ratio of these totals (since dividing both by 5 cancels out, the ratio of averages equals the ratio of totals).

Step 1: Identify the number of males in Town X for each year

From the table, the number of males in Town X (in thousands) is:

2018 → 50
2019 → 52
2020 → 55
2021 → 53
2022 → 55

Step 2: Find the total (and average) number of males in Town X

$\text{Total (Town X)}=50+52+55+53+55=265$

$\text{Average (Town X)}=\frac{265}{5}=53$

Step 3: Identify the number of males in Town Y for each year

From the table, the number of males in Town Y (in thousands) is:

2018 → 53
2019 → 54
2020 → 55
2021 → 58
2022 → 62

Step 4: Find the total (and average) number of males in Town Y

$\text{Total (Town Y)}=53+54+55+58+62=282$

$\text{Average (Town Y)}=\frac{282}{5}=56.4$

Step 5: Form the ratio of the two averages

Since both averages are divided by the same number (5), the ratio of the averages equals the ratio of the totals:

$\text{Ratio}=\frac{265/5}{282/5}=\frac{265}{282}$

Step 6: Check if the ratio can be simplified

We check the GCD of 265 and 282.
265 = 5 × 53
282 = 2 × 3 × 47
Since 265 and 282 share no common factors, the ratio is already in its simplest form.

Therefore, the ratio of the average number of males in Town X to the average number of males in Town Y is 265 : 282.