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Solve the following question and mark the best possible option.
X, Y and Z can do a piece of work in 30 days. They all three worked for 4 days and then X left. Y and Z continued the work and worked for 20 more days when Y left. Z worked for another 80 days and completed the work. In how many days can X alone complete the work if Z can complete it in 150 days?
- a)30 days
- b)60 days
- c)40 days
- d)50 days
Correct answer is option 'B'. Can you explain this answer?
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Verified Answer
Solve the following question and mark the best possible option.X, Y an...
Assume the total work to be 1200 units. (LCM of all the numbers)
Then Z’s 1 day work = 8 units.
Then Z’s 1 day work = 8 units.
⇒ (X + Y + Z)’s 1 day work = 40 units.
X, Y, Z work together in the first 4 days
⇒Work done in the first 4 days = 40 × 4 = 160 units
Z alone works during the last 80 days
⇒Work done in the last 80 days = 80 × 8 = 640 units
Remaining work = 1200 – (160 + 640) = 400 units
This work is done by Y and Z in 20 days.
This work is done by Y and Z in 20 days.
⇒ (Y + Z)’s 1 day work = 20 units
⇒X’s 1 day work = (X + Y + Z)’s 1 day work – (Y + Z)’s 1 day work = 40 units – 20 units = 20 units
⇒X can do the work of 1200 units in 60 days.
Most Upvoted Answer
Solve the following question and mark the best possible option.X, Y an...
To solve this question, let's first determine the work efficiency of each person. Since X, Y, and Z can complete the work together in 30 days, their combined efficiency per day is 1/30.
Let's assume that X's efficiency per day is x, Y's efficiency per day is y, and Z's efficiency per day is z.
1. Work done by X, Y, and Z in 4 days:
Since they work together for 4 days, the total work done by them is (1/30) * 4 = 4/30.
2. Work done by Y and Z in 20 days:
After X leaves, Y and Z continue the work. So, their combined efficiency per day is (y + z). Therefore, the work done by Y and Z in 20 days is (y + z) * 20.
3. Work done by Z in 80 days:
After Y leaves, Z works alone. So, the work done by Z in 80 days is z * 80.
Now, let's determine the remaining work that X needs to complete alone.
Remaining work = Total work - Work done by X, Y, and Z in 4 days - Work done by Y and Z in 20 days - Work done by Z in 80 days
Remaining work = 1 - 4/30 - (y + z) * 20 - z * 80
Since Z can complete the work alone in 150 days, his efficiency per day is 1/150. Therefore, z = 1/150.
Substituting the value of z in the equation for remaining work:
Remaining work = 1 - 4/30 - (y + 1/150) * 20 - 1/150 * 80
Simplifying the equation, we get:
Remaining work = 1 - 2/15 - (y + 1/150) * 2 - 4/75
Now, we know that the remaining work needs to be completed by X alone. So, the equation becomes:
Remaining work = x * D
where D is the number of days X takes to complete the remaining work.
Substituting the value of remaining work in the equation:
x * D = 1 - 2/15 - (y + 1/150) * 2 - 4/75
Now, we need to find the value of D, which represents the number of days X takes to complete the work. To do that, we need to know the value of x and y, which are not given in the question.
Therefore, the given information is insufficient to determine the number of days X takes to complete the work.
Let's assume that X's efficiency per day is x, Y's efficiency per day is y, and Z's efficiency per day is z.
1. Work done by X, Y, and Z in 4 days:
Since they work together for 4 days, the total work done by them is (1/30) * 4 = 4/30.
2. Work done by Y and Z in 20 days:
After X leaves, Y and Z continue the work. So, their combined efficiency per day is (y + z). Therefore, the work done by Y and Z in 20 days is (y + z) * 20.
3. Work done by Z in 80 days:
After Y leaves, Z works alone. So, the work done by Z in 80 days is z * 80.
Now, let's determine the remaining work that X needs to complete alone.
Remaining work = Total work - Work done by X, Y, and Z in 4 days - Work done by Y and Z in 20 days - Work done by Z in 80 days
Remaining work = 1 - 4/30 - (y + z) * 20 - z * 80
Since Z can complete the work alone in 150 days, his efficiency per day is 1/150. Therefore, z = 1/150.
Substituting the value of z in the equation for remaining work:
Remaining work = 1 - 4/30 - (y + 1/150) * 20 - 1/150 * 80
Simplifying the equation, we get:
Remaining work = 1 - 2/15 - (y + 1/150) * 2 - 4/75
Now, we know that the remaining work needs to be completed by X alone. So, the equation becomes:
Remaining work = x * D
where D is the number of days X takes to complete the remaining work.
Substituting the value of remaining work in the equation:
x * D = 1 - 2/15 - (y + 1/150) * 2 - 4/75
Now, we need to find the value of D, which represents the number of days X takes to complete the work. To do that, we need to know the value of x and y, which are not given in the question.
Therefore, the given information is insufficient to determine the number of days X takes to complete the work.
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Solve the following question and mark the best possible option.X, Y and Z can do a piece of work in 30 days. They all three worked for 4 days and then X left. Y and Z continued the work and worked for 20 more days when Y left. Z worked for another 80 days and completed the work. In how many days can X alone complete the work if Z can complete it in 150 days?a)30 daysb)60daysc)40 daysd)50 daysCorrect answer is option 'B'. Can you explain this answer?
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Solve the following question and mark the best possible option.X, Y and Z can do a piece of work in 30 days. They all three worked for 4 days and then X left. Y and Z continued the work and worked for 20 more days when Y left. Z worked for another 80 days and completed the work. In how many days can X alone complete the work if Z can complete it in 150 days?a)30 daysb)60daysc)40 daysd)50 daysCorrect answer is option 'B'. Can you explain this answer? for CAT 2024 is part of CAT preparation. The Question and answers have been prepared according to the CAT exam syllabus. Information about Solve the following question and mark the best possible option.X, Y and Z can do a piece of work in 30 days. They all three worked for 4 days and then X left. Y and Z continued the work and worked for 20 more days when Y left. Z worked for another 80 days and completed the work. In how many days can X alone complete the work if Z can complete it in 150 days?a)30 daysb)60daysc)40 daysd)50 daysCorrect answer is option 'B'. Can you explain this answer? covers all topics & solutions for CAT 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Solve the following question and mark the best possible option.X, Y and Z can do a piece of work in 30 days. They all three worked for 4 days and then X left. Y and Z continued the work and worked for 20 more days when Y left. Z worked for another 80 days and completed the work. In how many days can X alone complete the work if Z can complete it in 150 days?a)30 daysb)60daysc)40 daysd)50 daysCorrect answer is option 'B'. Can you explain this answer?.
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