Problem:
To obtain 4 liters of a 5N HCl solution, we need to determine the volumes of 10N HCl and 2N HCl that should be mixed together.

Solution:

Step 1: Understand the problem:
- We need to create a 5N HCl solution.
- We have two different concentrations of HCl available: 10N and 2N.
- We need to find the volumes of these two solutions that should be mixed to obtain 4 liters of the desired concentration.

Step 2: Determine the number of moles of HCl required:
- To calculate the volume of each solution, we need to know the number of moles of HCl required.
- The equation for molarity (M) is defined as Moles of solute / Volume of solution (in liters).
- Given that we need a 4-liter solution with a concentration of 5N, we can calculate the number of moles required as follows:
Moles of HCl = Molarity × Volume of solution
Moles of HCl = 5N × 4 L
Moles of HCl = 20 moles

Step 3: Determine the volume of 10N HCl:
- We know the number of moles required (20 moles) and the concentration of the 10N HCl solution.
- Using the equation mentioned in step 2, we can calculate the volume of 10N HCl required:
Moles of HCl = Molarity × Volume of solution
20 moles = 10N × Volume of 10N HCl
Volume of 10N HCl = 20 moles / 10N
Volume of 10N HCl = 2 liters

Step 4: Determine the volume of 2N HCl:
- We need to find the volume of 2N HCl required to make up the remaining volume of the solution (4 liters - 2 liters).
- The concentration of the 2N HCl solution is given, and we already know the number of moles required (20 moles).
- Using the same equation as in step 2, we can calculate the volume of 2N HCl required:
Moles of HCl = Molarity × Volume of solution
20 moles = 2N × Volume of 2N HCl
Volume of 2N HCl = 20 moles / 2N
Volume of 2N HCl = 10 liters

Step 5: Determine the final volumes of each solution:
- We have calculated that we need 2 liters of 10N HCl and 10 liters of 2N HCl.
- To obtain the final 4-liter solution, we mix these volumes together:
Volume of 10N HCl = 2 liters
Volume of 2N HCl = 10 liters

Conclusion:
To obtain a 4-liter 5N HCl solution, we need to mix 2 liters of 10N HCl and 10 liters of 2N HCl.