During a spring vacation, it rained on 13 days. When it rained in the morning, the afternoon was sunny. Every rainy afternoon was preceded by a sunny morning. There were 11 sunny mornings and 12 sunny afternoons. How long was the vacation?

The holiday lasted for 18 days.

Explanation:

Let's assume the number of days are as following:

let the rain in the morning and lovely afternoon = X days

Clear morning and rain in the afternoon = Y days

No rain in the morning and in the afternoon = Z days

Now according to the question

Number of days with rain = X + Y = 13 days

Number of days with clear mornings = Y + Z = 11 days

Number of days with clear afternoons = X + Z = 12 days

Solving above 3 equations, we get

X = 7, Y = 6 and Z = 5

Now total number of days on holiday = X+Y+Z = 7+6+5 = 18

Hence, total number of days on holiday = 18 days.