Question Details

Carefully analyze the given details and answer the question that follows.

There are three branches (Branch A, Branch B, and Branch C) in enterprise K. The ratio of male to female employees in Branch A is 7:10. The number of female employees in Branch C is 20% more than the number of female employees in Branch A. The number of male employees in Branch C is six more than that of female employees in Branch C. The average number of male employees across all three branches is 39 and the number of male employees in Branch B is 35. The number of female employees in Branch B is 25% more than the number of female employees in Branch C.

The number of male and female employees in Branch D is 40% and 20% more than the number of male and female employees in Branch B respectively. Find the total number of employees in Branch D.

Options

A

121

B

141

C

101

D

129

E

114

Show Answer

Correct Answer :

Option A

121

Solution :

The correct answer is 121.

Step 1: Express the employees of Branch A and Branch C in terms of a variable.
Let the ratio multiplier for male and female employees in Branch A be x.
Ratio of male to female employees in Branch A = 7 : 10.
Number of male employees in Branch A, MA=7x
Number of female employees in Branch A, FA=10x

The number of female employees in Branch C is 20% more than in Branch A:
FC=10x×1.20=12x

The number of male employees in Branch C is 6 more than the female employees in Branch C:
MC=12x+6

Step 2: Solve for x using the average number of male employees.
We are given that the number of male employees in Branch B, MB=35, and the average number of male employees across all three branches (A, B, and C) is 39.
MA+MB+MC3=39
7x+35+(12x+6)=39×3
19x+41=117
19x=11741
19x=76
x=4

Step 3: Calculate female employees in Branch C and Branch B.
Female employees in Branch C:
FC=12×4=48
Female employees in Branch B are 25% more than female employees in Branch C:
FB=48×1.25=60

Step 4: Find male and female employees in Branch D.
Male employees in Branch D are 40% more than male employees in Branch B (MB=35):
MD=35×1.40=49
Female employees in Branch D are 20% more than female employees in Branch B (FB=60):
FD=60×1.20=72

Step 5: Calculate total employees in Branch D.
Total employees in Branch D=MD+FD=49+72=121

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