Comprehension

Directions: Read the data carefully and answer the following questions. 

The table given below shows the total number of Male and Female employees in five different companies ('A', 'B', 'C', 'D' and 'E'). It also shows the ratio of the number of Male employees to female employees in each company.

Companies Total Number of Employees Ratio of Male to Female Employees
A 624 7:6
B 936 5:8
C 630 4:3
D 528 5:6
E 600 3:2

 

If Company A and Company C decide to merge, and Company D and Company E decide to merge, what is the approximate difference between the average number of male employees in the merged Company (A+C) and the average number of female employees in the merged Company (D+E)?

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  1. 38
  2. 49
  3. 62
  4. 95
  5. 84

Answer (Detailed Solution Below)

Option 5 : 84
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Detailed Solution

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General Solution:

Company A:

Total employees = 624

Ratio of Male to Female = 7 : 6

Total parts = 7 + 6 = 13

Males = 7 / 13 × 624 = 336

Females = 6 / 13 × 624 = 288

Company B:

Total employees = 936

Ratio of Male to Female = 5 : 8

Total parts = 5 + 8 = 13

Males = 5 / 13 × 936 = 360

Females = 8 / 13 × 936 = 576

Company C:

Total employees = 630

Ratio of Male to Female = 4 : 3

Total parts = 4 + 3 = 7

Males = 4 / 7 × 630 = 360

Females = 3 / 7 × 630 = 270

Company D:

Total employees = 528

Ratio of Male to Female = 5 : 6

Total parts = 5 + 6 = 11

Males = 5 / 11 × 528 = 240

Females = 6 / 11 × 528 = 288

Company E:

Total employees = 600

Ratio of Male to Female = 3 : 2

Total parts =3 + 2 = 5

Males = 3 / 5 × 600 = 360

Females = 2 / 5 × 600 = 240

Thus,

Company Total Employees Males Females
A 624 336 288
B 936 360 576
C 630 360 270
D 528 240 288
E 600 360 240

 

Calculations:

Merged Company A+C:

Males in A = 336

Males in C = 360

Total males in A+C = 336 + 360 = 696

Females in A = 288

Females in C = 270

Total females in A+C = 288 + 270 = 558

Merged Company D+E:

Males in D = 240

Males in E = 360

Total males in D+E =240 + 360 = 600

Females in D = 288

Females in E = 240

Total females in D+E =288 + 240 = 528

Average Number of Male Employees in (A+C):

Average Males in A+C = Total Males in A+C / Number of Companies = 696 / 2 = 348

Average Number of Female Employees in D+E:

Average Females in D+E = Total Females in D+E / Number of Companies = 528 / 2 = 264

Difference = Average Males in A+C - Average Females in D+E = 348 - 264 = 84

Thus, the approximate difference between the average number of male employees in the merged Company A+C and the average number of female employees in the merged Company D+E is 84.

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