# Difficult Number System Solved QuestionAptitude Discussion

 Q. Ram and Shyam take a vacation at their grandparents' house. During the vacation, they do any activity together. They either played tennis in the evening or practiced Yoga in the morning, ensuring that they do not undertake both the activities on any single day. There were some days when they did nothing. Out of the days that they stayed at their grandparents' house, they involved in one of the two activities on 22 days. However, their grandmother while sending an end of vacation report to their parents stated that they did not do anything on 24 mornings and they did nothing on 12 evenings. How long was their vacation?
 ✖ A. 36 days ✖ B. 14 days ✔ C. 29 days ✖ D. Cannot be determined

Solution:
Option(C) is correct

Before we go to solution, few words.

The question given above appeared in CAT 2002. It is an interesting question in framing a set of simple equations from the information given in the question and solving it. The catch is in understanding the language of the question properly so that you frame the question correctly. Once, the equations are framed the question will take not more than 45 seconds to get the answer. So, do not lose focus while reading the question. Understand it properly and then answer the question.

Enough said, back to question now.

Let the number of days that they holidayed be equal to $T$.

Then, they practiced Yoga on $(T – 24)$ mornings.
They played tennis on $(T – 12)$ evenings.

As they did not do both the activities together on any single day,

$\text{Days on which they had any activity}$
$=\text{Number of days they practiced Yoga} +$
$\text{ Number of days they played tennis}$
i.e., $22 = T – 24 + T – 12$
or $22 + 24 +12 = 2T$
or $58 = 2T$

Hence, $T =$ 29 Days.

## (2) Comment(s)

Zia
()

What about the number of days when they did nothing?

In my opinion, the answer should be 34 which is not in options.

There are 24 mornings & 12 evenings when they did nothing. So there were 12 complete days when the two were free. 12 mornings are left so in the evening of those 12 mornings they played tennis. They did all the activities together for 22 days. If they played tennis on 12 evenings so they did Yoga for 22-12= 10 day's morning. In total, 12 days of nothing + 12 evenings of tennis + 10 mornings of Yoga makes 34 days.

Hope I did the solution right?

Hamza
()

No Zia, you seem to be mistaken.

You say, "There are 24 mornings & 12 evenings when they did nothing. So there were 12 complete days when the two were free". How do you arrive at this?

Now, about your question related to the number of days when they did nothing. Since total stay was of 29 days and they were involved in one the activities for 22 days.

So, they were NOT involved in any of the activity for 29-22= 7 days or 1 week.

I find 29 to be the correct answer.