In an office of 900 employees, on a particular day, except for 10% of the female employees, all employees were present. On the next day, except for 8% of the male employees, all employees were present. The number of employees present on each of these two days was the same. Find the total number of male employees on the payroll of this office.

Let's assume the number of male and female employees working in the office is 'M' and 'F' respectively.

In an office of 900 employees.

M+F = 900    Eq.(i)

on a particular day, except for 10% of the female employees, all employees were present.

M+(100-10)% of F    Eq.(ii)

On the next day, except for 8% of the male employees, all employees were present.

(100-8)% of M+F    Eq.(iii)

The number of employees present on each of these two days was the same.

So Eq.(ii) = Eq.(iii)

M+(100-10)% of F = (100-8)% of M+F

M+90% of F = 92% of M+F

M+0.9F = 0.92M+F

M-0.92M = F-0.9F

0.08M = 0.1F

F = 0.8M    Eq.(iv)

Put Eq.(iv) in Eq.(i)

M+0.8M = 900

1.8M = 900

$$M=\frac{900}{1.8}$$

$$M=\frac{9000}{18}$$

M = 500

Total number of male employees on the payroll of this office = 500