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Sagot :
We will solve this problem by solving the system of equations formed by the statements given in the question.
Number of male and female officers are 200 and 140 respectively.
Statements given in the question,
- There are 60 more male officers than female officers.
- Ratio of male and female officers is 10 : 7.
Let the number of male officers in the police force = m
And the female officers in the police force = f
"There are 60 male officers than female officers"
m = f + 60 ----- (1)
"Ratio of male and female officers is 10 : 7"
Therefore, [tex]\frac{m}{f}=\frac{10}{7}[/tex]
[tex]m=\frac{10}{7}f[/tex] ------- (2)
By substituting the value of 'm' from equation (2) to equation (1),
[tex]\frac{10}{7}f=f+60[/tex]
[tex]\frac{10}{7}f-f=60[/tex]
[tex]\frac{3}{7}f=60[/tex]
[tex]f=140[/tex]
Substitute the value of 'f' in equation (1),
m = 140 + 60
m = 200
Therefore, number of male and female officers are 200 and 140 respectively.
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