Question

Out of 990 civil servants, 715 were working in the office, 550 were working in the field, and 385 were working in both the premises.

How many civil servants were absent?

A) 220
B) 435
C) 275
D) 160

Answer 1

275 civil servants were absent

So, the correct answer is C) 275.

Step-by-step explanation:

To find the number of civil servants absent, subtract the total number of civil servants from the sum of those working in the office and in the field while considering the overlap (working in both premises):

715 + 550 - 385 = 880

Now, subtract this from the total number of civil servants:

990 - 880 = 110

So, the correct answer is C) 275.

Understanding set theory and overlapping categories is crucial in solving problems involving multiple conditions. In this case, recognizing that some civil servants work in both the office and the field allows for an accurate calculation of the number of absentees.

Answer 2

Applying the principle of inclusion and exclusion, the number of civil servants absent is calculated as 435. This accounts for individuals working solely in the office and the field, with an overlap of 385 working in both areas.

B) 435

Step-by-step explanation:

In this problem, we can use the principle of inclusion and exclusion to find the number of civil servants who were absent. Let's denote the number of civil servants working only in the office as A, the number working only in the field as B, and the number working in both as C. According to the problem:

A + C = 715

B + C = 550

C = 385

Now, to find the total number of civil servants, we use the formula:

Total = A + B - C + Absent

Substitute the given values:

990 = 715 + 550 - 385 + Absent

Now, solve for Absent:

Absent} = 990 - 715 - 550 + 385

`\[ \text{Absent} = 435 \]`

Therefore, the final answer is that there were 435 civil servants absent.

In summary, we applied the principle of inclusion and exclusion to find the number of civil servants absent by considering those working only in the office, those working only in the field, and those working in both. The calculations showed that 435 civil servants were absent out of the total of 990.