Question

In a rainy season, Jamshedpur experienced some rain for thirteen days. A morning rain was always followed by a clear evening. An evening rain was always preceded by a clear morning. A total of 9 mornings and 12 evenings were clear. How many rainless days did Jamshedpur have in the period?

• A. 7
• B. 6
• C. 5
• D. 3

Hint:

Compare the number of clear mornings with the number of clear evenings. The gap between the two counts points to the days that had no rain at all.

Answer 1

The Correct Option is D

Every day in the 13-day spell is one of three kinds: rain in the morning followed by a clear evening, since a morning rain is always followed by a clear evening, rain in the evening that was preceded by a clear morning, since an evening rain is always preceded by a clear morning, or a fully rainless day with both a clear morning and a clear evening.

We are told 9 mornings were clear. A clear morning happens only on an evening-rain day or on a rainless day, since a morning-rain day by definition has rain in the morning and cannot be counted here, so this count of 9 bundles those two kinds of days together, evening-rain days and rainless days.

We are also told 12 evenings were clear, which is 3 more than the 9 clear mornings. A clear evening happens only on a morning-rain day or a rainless day, since an evening-rain day by definition has rain in the evening, so this count of 12 bundles morning-rain days and rainless days together instead.

Comparing the two bundles, the extra count of 3 clear evenings, beyond what the 9 clear mornings already cover, comes from the days that had no rain in them at all, since those are the only days that get counted in both totals without being offset by a rain-carrying day on the other side.

So the number of rainless days is $12 - 9 = 3$.

Let's summarize:

• Clear mornings, 9 in all, come from evening-rain days plus rainless days.
• Clear evenings, 12 in all, come from morning-rain days plus rainless days.
• The gap between these two totals, 3, gives the number of rainless days.

Thus, Jamshedpur had 3 days with no rain at all during this period.