The 200 mL solution of NaOH with a molarity of M/4 has a density of 1.08 g/cm^3. The molarity of the solution is required after 5 g of NaOH is added to it.
To determine the resultant molarity we do not need the density of the solution. We need the molar mass of NaOH. Sodium hydroxide has a molar mass of 40 g/mole. 5 g of NaOH is equivalent to 5/40 = 1/8 mole.
The original solution contained 1/4 mole of NaOH per liter. 200 mL had 1/20 moles. On adding 1/8 mole, the total number of moles of NaOH in the 200 mL of liquid is 1/20 + 1/8 = 7/40.
This gives a molarity of (7/40)*1000/200 = 7/8
The resultant molarity of the solution on adding 5 g of NaOH is 7/8 M.