Number Properties : Word Problem

The question given below 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.

Question

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?

1. 36 days
2. 14 days
3. 19 days
4. Cannot be determined
   
   

Correct Choice is (3) and Correct Answer is 19 days

Explanatory Answer

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,

Days on which they had any activity = Number of days they practiced Yoga + Number of days they played tennis

i.e., 22 = T – 24 + T – 12

or 22 + 24 +12 = 2T

or 58 = 2T

Hence, T = 29.

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CAT Practice Questions and Answers : Listed Topicwise

Number Theory		Permutation & Probability		Data sufficiency		Inequalities
Geometry		Mensuration		Trigonometry		Coordinate Geometry
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Speed Time Distance		Pipes Cisterns		Linear Quadratic		Races
Progressions, AP & GP		New Topic		New Topic		New Topic