The cost to replace a washing machine outlet box for the drain outlet and the incoming water lines range from $40.00 to $100.00 or so if you do it yourself.
If you hire a plumber or handyman to replace the washing machine outlet box the cost can be between $150.00 to $300.00 for parts and labor.
The cost to replace an electrical outlet for the washing machine can cost around $100.00 to $150.00 for the labor and parts if an electrician does the job.
Or if you do it yourself you can replace the electrical outlet for around a few dollars and your time.
A washing machine cannot share an outlet and needs a dedicated circuit.
According to electrical code any receptacles or electrical outlets in a laundry room must be on 20 AMP circuits and not shared with any other outlets including lighting.
The lighting must also be on a separate circuit than the washing machine and other outlets.
This is according to electrical codes and building codes.
However you can plug a washing machine into an outlet that is shared with other low wattage appliances or lights.
You just can't wire it that way now and pass inspection.
My washing machine is on a circuit of it's own and it also has a light above the washing machine tied into it which is fine.
I've also had washing machines in older houses tied into outlets connected with other low wattage appliances and it worked fine as the washing machine is not all that power hungry.
But you should always use the washing machine when possible on a dedicated circuit.
Avoid plugging the washing machine into any power strips that could get overloaded and start a fire.