A family X went for a vacation. Unfortunately it rained for 13 days when they…

Concept

On any day, rain and clear weather never occur in both the morning and the afternoon together — if it rains in one session, the other session that day is clear; a day with no rain at all has both sessions clear. So every day contributes exactly two half-day sessions (one morning + one afternoon) to the total count of sessions.

Application

1. The family enjoyed clear weather in 11 mornings and 12 afternoons, so total clear half-days = 11 + 12 = 23.

2. It rained on 13 days, and rain occupies exactly one half-day session per rainy day, contributing 13 rainy half-days.

3. Total half-day sessions across the whole stay = 23 (clear) + 13 (rainy) = 36.

4. Since each day equals 2 half-day sessions, total number of days = 36 / 2 = 18.

Cross-check

Let a = days it rained only in the morning (afternoon clear), b = days it rained only in the afternoon (morning clear), and c = days with no rain at all (both sessions clear).

• a + b = 13 (total rainy days).

• Clear mornings = b + c = 11; clear afternoons = a + c = 12.

• Adding these: a + b + 2c = 23, so 13 + 2c = 23, giving c = 5.

• Total days = a + b + c = 13 + 5 = 18 — confirming the half-day method.