Question Analysis:
The given question asks us to determine how many marriage anniversaries would fall on a Sunday in the next 15 years, given that the couple was married on 18.09.1977, which was a Sunday.

Given Information:
- The couple was married on 18.09.1977, which was a Sunday.

Approach:
To solve this problem, we need to find the number of Sundays in the next 15 years after 18.09.1977. We can calculate this by counting the number of leap years and non-leap years in the given time period, as the number of days in a year affects the number of Sundays.

Solution:

Step 1: Count the Number of Leap Years:
- Leap years occur every 4 years.
- Since the given time period is 15 years, we have 15/4 = 3 leap years.

Step 2: Count the Number of Non-Leap Years:
- The remaining years after considering the leap years are 15 - 3 = 12 non-leap years.

Step 3: Calculate the Total Number of Days:
- Leap years have one extra day, so the total number of days in leap years is 3 * 366 = 1098 days.
- Non-leap years have 365 days each, so the total number of days in non-leap years is 12 * 365 = 4380 days.

Step 4: Calculate the Number of Sundays:
- Since the couple was married on a Sunday, every 7th day after the wedding anniversary will be a Sunday.
- The total number of days in the given time period is 1098 + 4380 = 5478 days.
- The number of Sundays in 5478 days is 5478 / 7 = 782 Sundays.

Step 5: Determine the Number of Marriage Anniversaries on Sunday:
- Since the first anniversary falls on the same day as the wedding day, there is one marriage anniversary on a Sunday.
- The second anniversary will be on the same day of the week as the wedding day if there are 7 days in between, which happens when the year is a non-leap year. So, one more anniversary falls on a Sunday.
- Therefore, the number of marriage anniversaries that fall on a Sunday is 2.

Final Answer:
The number of marriage anniversaries that fall on a Sunday in the next 15 years is 2 (option B).