The number of male employees from city B is ______ % of the total number of…

In a distribution table each percentage must be applied to the base that its own column is measured against: a share listed under the employee-distribution column is a share of the overall employee total, while a share listed under the female-employee-distribution column is a share of the overall female total. Within any city, male employees equal that city's total employees minus that city's female employees. Any headcount is converted into a percentage of the grand total by dividing it by the grand total and multiplying by 100.

1. Split the grand total by the given gender ratio. With 80,000 employees in the ratio male : female = 9 : 7, male employees = (9/16) x 80,000 = 45,000 and female employees = (7/16) x 80,000 = 35,000.

2. Read city B's share from the employee-distribution column, whose base is the overall employee total: city B's employees = 15% of 80,000 = 12,000.

3. Read city B's share from the female-employee-distribution column, whose base is the overall female total: city B's female employees = 18% of 35,000 = 6,300.

4. Subtract the female count from the city total to get the male count: city B's male employees = 12,000 - 6,300 = 5,700.

5. Express that headcount as a percentage of all employees in the six cities: (5,700 / 80,000) x 100 = 7.125%.

Verify the result in two independent ways. Reversing the last step, 7.125% of 80,000 gives back 5,700 male employees. Adding the two parts of city B, 5,700 + 6,300 = 12,000, which is exactly the 15% of 80,000 that city B contributes, so the male and female counts reconstruct the city total.

• Applying the 18% female share to city B's own 12,000 employees gives 2,160; that uses the city total as the base instead of the overall female total of 35,000.

• Applying the 18% female share to the grand total of 80,000 gives 14,400, which is larger than city B's entire workforce and therefore cannot be its female count.

• Reading the ratio 9 : 7 in the reverse order makes the female total 45,000 and distorts every step that follows.

• The graduate columns (33% male graduates and 37% female graduates for city B) describe only the graduate subset within the city and are not used in a headcount question.