The Spoilt Holiday

            A group of friends and me went on a holiday to a hill station. It rained for 13 days. But when it rained in the morning the afternoon was lovely. And when it rained in the afternoon the day was preceded by a clear morning.

          Altogether there were 11 very nice mornings and 12 very nice afternoons. How many days did our holiday last?

Answer: Our holiday lasted for 18 days. First of all let us see how many possible types of days there could be. There could only be three such as: 

             Rain in the morning and fine in the afternoon 

       Fine in the morning and fine in the afternoon 

           Fine in the morning and rain in the afternoon

Let us assume the number of such days in each category be a, b and c.

Then: Number of days on which rain falls = a + c = 13

Number of days with fine mornings = b +c = 11

Number of days with fine afternoons = a + b = 12

We derive from these equations that:

A=7,   b = 5, c = 6

 Therefore the number of days on holiday is:

 7+ 5+ 6 + 18