Question:

1/3 of the workforce of a cricket stadium is working on the ground and 5/6 of the remaining work forces is taking care of security. The remaining 6 workers are working in the seating area. Thus, Find the total strength of workforce of the stadium.

Answer:

Let the total strength of workforce of the stadium be x.

Since, 1/3 of the workforce is working on the ground, So;

Workers working on the ground = [tex]\frac{1}{3} x\\[/tex]

Now, The remaining 2/3 of the workforce is left, so:

Workers remaining = [tex]\frac{2}{3} x[/tex]

5/6 of the remaining workforce is taking care of security, So:

Workers taking care of security = [tex](\frac{5}{6} )(\frac{2}{3} )x[/tex]  OR  [tex]\frac{5}{9} x[/tex]

Thus, the number of workers left after security work is: [tex](\frac{2}{3} )x - (\frac{5}{9} )x = \frac{1}{9} x[/tex]

The problem states that there were 6 workers working in the seating area, which is equals to [tex]\frac{1}{9} x[/tex].

Solving for x, we get:

[tex]\frac{1}{9}x = 6 \\x = 6*9\\[/tex]

x = 54

Therefore, the total strength of the workforce of the stadium is 54.