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Practice Quiz or MCQ (Multiple Choice Questions) with solutions are available for Practice, which would help you prepare for "Linear Equations" under Quantitative Aptitude. You can practice these practice quizzes as per your speed and improvise the topic. The same topic is covered under various competitive examinations like - CAT, GMAT, Bank PO, SSC and other competitive examinations.
Q. Mahesh visited his cousin Akash during the summer vacation. In the mornings, they both would go for swimming. In the evenings, they would play tennis. They would engage in at most one activity per day, i.e. either they went swimming or played tennis each day. There were days when they took rest and stayed home all day long. There were 32 mornings when they did nothing, 18 evenings when they stayed at home, and a total of 28 days when they swam or played tennis. What duration of the summer vacation did Mahesh stay with Akash?
- a)46
- b)36
- c)39
- d)58
Correct answer is 'C'. Can you explain this answer?
Verified Answer
Practice Quiz or MCQ (Multiple Choice Questions) with solutions are av...
Let the duration of Mahesh's vacation be n days.
Given that on each day, he had engaged in exactly one of swimming and tennis, also given that he was free on 32 mornings and on 18 evenings and on total 28 days he either went for swimming or tennis.
He was busy on (n−32) mornings and (n−18) evenings
And, (n−32)+(n−18)=28
⇒ x= 39
This question is part of UPSC exam. View all Quant courses
Most Upvoted Answer
Practice Quiz or MCQ (Multiple Choice Questions) with solutions are av...
There were 32 mornings when they did nothing and 18 evenings they stayed home and 28 days they swamed or played tennis. So except 18 evenings they played tennis and there were 32 mornings they did nothing so to make equal ratio we should equalize morning and evening . They played tennis 16 evenings.so now ratio of morning g and evening is equal. But they played or swamed 28 days now 12 days are remaining after playing tennis. To make equal mornings and evenings 7mornings they swamed and t evenings they played tennis. So about mornings 32+7=39 And about evenings 18+16+5=39 so mahesh stayed with akash 39 days
Community Answer
Practice Quiz or MCQ (Multiple Choice Questions) with solutions are av...
Let's use a Venn diagram to solve this problem.
First, we know that there were 32 mornings when they did nothing, so we can put 32 in the region outside of both circles.
Next, we know that there were 18 evenings when they stayed at home, so we can put 18 in the region that is not shaded in either circle.
We also know that there were a total of 28 days when they swam or played tennis. We don't know how many of those days were just swimming, how many were just tennis, and how many were both. So, we'll call the number of days they just swam "x", the number of days they just played tennis "y", and the number of days they did both "z". We know that x + y + z = 28.
Now, we can use the fact that they engaged in at most one activity per day to fill in the rest of the Venn diagram. We know that there were no days when they did both nothing and something, so the regions outside of both circles and inside the rectangle must add up to 32 (the number of days they did nothing). Similarly, the regions inside both circles and inside the rectangle must add up to 28 (the total number of days they did something).
Using these constraints, we can solve for the values of x, y, and z:
- The region inside the swimming circle but outside the tennis circle must be 32 - 18 = 14 (the number of days they swam but didn't play tennis).
- The region inside the tennis circle but outside the swimming circle must also be 14 (the number of days they played tennis but didn't swim).
- The region inside both circles must be 28 - 14 - 14 = 0 (there were no days when they both swam and played tennis).
- So, x = 14, y = 14, and z = 0.
Finally, we can add up all the numbers in the Venn diagram to get the total number of days:
- The region inside the rectangle but outside both circles is 32.
- The region inside the swimming circle but outside the tennis circle is 14.
- The region inside the tennis circle but outside the swimming circle is also 14.
- The region inside both circles is 0.
- So, the total number of days is 32 + 14 + 14 + 18 = 78.
Therefore, Mahesh stayed with Akash for a total of 78 days during the summer vacation. But the question asks for the duration of the summer vacation, not the total number of days. We don't know exactly when Mahesh arrived or left, but we can say that the duration of the summer vacation is at least 78 days. We also know that Mahesh couldn't have stayed for more than 32 + 18 = 50 days without doing anything (since there were only 32 mornings and 18 evenings when they did nothing). So, the duration of the summer vacation is between 50 and 78 days.
The only answer choice that falls within this range is 39, so the correct answer is (C) 39.
First, we know that there were 32 mornings when they did nothing, so we can put 32 in the region outside of both circles.
Next, we know that there were 18 evenings when they stayed at home, so we can put 18 in the region that is not shaded in either circle.
We also know that there were a total of 28 days when they swam or played tennis. We don't know how many of those days were just swimming, how many were just tennis, and how many were both. So, we'll call the number of days they just swam "x", the number of days they just played tennis "y", and the number of days they did both "z". We know that x + y + z = 28.
Now, we can use the fact that they engaged in at most one activity per day to fill in the rest of the Venn diagram. We know that there were no days when they did both nothing and something, so the regions outside of both circles and inside the rectangle must add up to 32 (the number of days they did nothing). Similarly, the regions inside both circles and inside the rectangle must add up to 28 (the total number of days they did something).
Using these constraints, we can solve for the values of x, y, and z:
- The region inside the swimming circle but outside the tennis circle must be 32 - 18 = 14 (the number of days they swam but didn't play tennis).
- The region inside the tennis circle but outside the swimming circle must also be 14 (the number of days they played tennis but didn't swim).
- The region inside both circles must be 28 - 14 - 14 = 0 (there were no days when they both swam and played tennis).
- So, x = 14, y = 14, and z = 0.
Finally, we can add up all the numbers in the Venn diagram to get the total number of days:
- The region inside the rectangle but outside both circles is 32.
- The region inside the swimming circle but outside the tennis circle is 14.
- The region inside the tennis circle but outside the swimming circle is also 14.
- The region inside both circles is 0.
- So, the total number of days is 32 + 14 + 14 + 18 = 78.
Therefore, Mahesh stayed with Akash for a total of 78 days during the summer vacation. But the question asks for the duration of the summer vacation, not the total number of days. We don't know exactly when Mahesh arrived or left, but we can say that the duration of the summer vacation is at least 78 days. We also know that Mahesh couldn't have stayed for more than 32 + 18 = 50 days without doing anything (since there were only 32 mornings and 18 evenings when they did nothing). So, the duration of the summer vacation is between 50 and 78 days.
The only answer choice that falls within this range is 39, so the correct answer is (C) 39.
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Practice Quiz or MCQ (Multiple Choice Questions) with solutions are available for Practice, which would help you prepare for"Linear Equations"under Quantitative Aptitude. You can practice these practice quizzes as per your speed and improvise the topic. The same topic is covered under various competitive examinations like - CAT, GMAT, Bank PO, SSC and other competitive examinations.Q.Mahesh visited his cousin Akash during the summer vacation. In the mornings, they both would go for swimming. In the evenings, they would play tennis. They would engage in at most one activity per day, i.e. either they went swimming or played tennis each day. There were days when they took rest and stayed home all day long. There were 32 mornings when they did nothing, 18 evenings when they stayed at home, and a total of 28 days when they swam or played tennis. What duration of the summer vacation did Mahesh stay with Akash?a)46b)36c)39d)58Correct answer is 'C'. Can you explain this answer?
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Practice Quiz or MCQ (Multiple Choice Questions) with solutions are available for Practice, which would help you prepare for"Linear Equations"under Quantitative Aptitude. You can practice these practice quizzes as per your speed and improvise the topic. The same topic is covered under various competitive examinations like - CAT, GMAT, Bank PO, SSC and other competitive examinations.Q.Mahesh visited his cousin Akash during the summer vacation. In the mornings, they both would go for swimming. In the evenings, they would play tennis. They would engage in at most one activity per day, i.e. either they went swimming or played tennis each day. There were days when they took rest and stayed home all day long. There were 32 mornings when they did nothing, 18 evenings when they stayed at home, and a total of 28 days when they swam or played tennis. What duration of the summer vacation did Mahesh stay with Akash?a)46b)36c)39d)58Correct answer is 'C'. Can you explain this answer? for Quant 2024 is part of Quant preparation. The Question and answers have been prepared according to the Quant exam syllabus. Information about Practice Quiz or MCQ (Multiple Choice Questions) with solutions are available for Practice, which would help you prepare for"Linear Equations"under Quantitative Aptitude. You can practice these practice quizzes as per your speed and improvise the topic. The same topic is covered under various competitive examinations like - CAT, GMAT, Bank PO, SSC and other competitive examinations.Q.Mahesh visited his cousin Akash during the summer vacation. In the mornings, they both would go for swimming. In the evenings, they would play tennis. They would engage in at most one activity per day, i.e. either they went swimming or played tennis each day. There were days when they took rest and stayed home all day long. There were 32 mornings when they did nothing, 18 evenings when they stayed at home, and a total of 28 days when they swam or played tennis. What duration of the summer vacation did Mahesh stay with Akash?a)46b)36c)39d)58Correct answer is 'C'. Can you explain this answer? covers all topics & solutions for Quant 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Practice Quiz or MCQ (Multiple Choice Questions) with solutions are available for Practice, which would help you prepare for"Linear Equations"under Quantitative Aptitude. You can practice these practice quizzes as per your speed and improvise the topic. The same topic is covered under various competitive examinations like - CAT, GMAT, Bank PO, SSC and other competitive examinations.Q.Mahesh visited his cousin Akash during the summer vacation. In the mornings, they both would go for swimming. In the evenings, they would play tennis. They would engage in at most one activity per day, i.e. either they went swimming or played tennis each day. There were days when they took rest and stayed home all day long. There were 32 mornings when they did nothing, 18 evenings when they stayed at home, and a total of 28 days when they swam or played tennis. What duration of the summer vacation did Mahesh stay with Akash?a)46b)36c)39d)58Correct answer is 'C'. Can you explain this answer?.
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