To find out how much they will have saved after 10 months, we can follow these steps:

1. Calculate the amount saved per month for each person:

- The man earns $N150,000$ per month, and saves 10%:
$$\text{Savings per month}=0.10\times 150,000=N15,000$$

- The wife earns $N125,000$ per month, and saves 10%:
$$\text{Savings per month}=0.10\times 125,000=N12,500$$

2. Calculate the total amount saved per month by both:

$$\text{Total monthly savings}=15,000+12,500=N27,500$$

3. Calculate the total savings over 10 months:

$$\text{Total savings}=27,500\times 10=N275,000$$

So, the amount they will have saved after 10 months is:

C. N275,000