This question is RELATED to calendars topic in aptitude.

Let me explain you in an easy and understandable way:

(1)

A leap year consists of 365 days.

1 week consists of 7-days.

7) 365 ( 52

    35

    -------

        15

        14

     ----------

          1.



That means a leap year will have 52 weeks + 1 odd day.




(2) 

A non-leap year consists of 366 days.

7) 366 ( 52

    35

    -------

        16

        14

   ---------

           2



That means a non-leap year consists of 52 weeks + 2 odd days.


(3)

100 years = 24 leap years + 76 non-leap years(100 - 24 = 76).

                 = 24 * 2 + 76 * 1

                 = 48 + 76

                 = 124.

In the next step, I will divide 124 with 7 because a week has 7 - days. 

7) 124 ( 1

    7

    ----

      54

       49

     --------

         5.
      
      

We can SEE that the remainder is 5. Therefore 100 years has 5 odd-days. 


Now,

26 years = 6 leap years + 20 non-leap years

               = 6 * 2 + 20 * 1

               = 12 + 20

               = 32.



Now,

Coming to your question:

126 years = 100 years + 26 years

                  = 5 + 32

                  = 37.


Now, Divide the RESULT by 7. Here we are dividing it by 7 because a week has 7 days.


7) 37(5

    35

    ---

     2

    ----




Therefore the number of odd days in 126 years = 2.


Hope this helps!