Final answer:
From the titration data, it can be concluded that the bases in the mixture are ammonium hydroxide and sodium hydroxide.
Step-by-step explanation:
The answer to the question can be determined by analyzing the titration data provided. From the information given, 25 mL of 0.1 N HCl is required to reach the endpoint of the phenolphthalein indicator, and 5 mL of HCl is required to reach the endpoint of the methyl orange indicator. Since the phenolphthalein indicator has an endpoint pH range between 8.2 and 10, and the methyl orange indicator has an endpoint pH range between 4.95 and 6, we can conclude that the first base in the mixture is a strong base with a pH range above 8.2 (such as sodium hydroxide (NaOH)), and the second base is a weak base with a pH range between 4.95 and 6 (such as ammonium hydroxide (NH4OH)). Therefore, the correct answer is (c) Ammonium hydroxide and sodium hydroxide.