An employer reduces the number of employees in the ratio 8:5 and increases their wages in the ration 7:9. therefore, the overall wages bill is:

To determine how the overall wage bill changes, we need to compare the initial total wage bill with the new total wage bill by calculating their ratio.

Step 1: Understand the given ratios
Let the initial number of employees be $E_1$ and the new number of employees be $E_2$.
The ratio of the reduction in the number of employees is given as 8:5.
$\frac{E_1}{E_2}=\frac{8}{5}$

Let the initial wage per employee be $W_1$ and the new wage per employee be $W_2$.
The ratio of the increase in wages is given as 7:9.
$\frac{W_1}{W_2}=\frac{7}{9}$

Step 2: Calculate the ratio of the total wage bill
The total wage bill is calculated by multiplying the number of employees by the wage per employee.

Initial total wage bill ($B_1$) = $E_1\times W_1$
New total wage bill ($B_2$) = $E_2\times W_2$

Now, find the ratio of the initial wage bill to the new wage bill:

$\frac{B_1}{B_2}=\frac{E_1\times W_1}{E_2\times W_2}=\left(\frac{E_1}{E_2}\right)\times \left(\frac{W_1}{W_2}\right)$

Substitute the given ratio values into the equation:

$\frac{B_1}{B_2}=\frac{8}{5}\times \frac{7}{9}=\frac{8\times 7}{5\times 9}=\frac{56}{45}$

Step 3: Conclusion
The ratio of the initial wage bill to the new wage bill is 56:45. Since the first value (56) is larger than the second value (45), the overall wage bill has decreased in the ratio 56:45.

Thus, the correct option is decreased in the ratio 56:45.