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A, B and C together started work on a task. After completing two-fifths of the work, C left while A and B worked together for 24 more days. C then replaced both A and B and completed the remaining work in 12 more days. If C alone takes 30 days to complete the work, in how many days can B alone complete the work? The rate at which A does work is twice the rate at which B does work.
- a)120
- b)180
- c)60
- d)360
- e)None of the above
Correct answer is option 'D'. Can you explain this answer?
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Verified Answer
A, B and C together started work on a task. After completing two-fifth...
Let the total work be 60 units.
Since C alone can complete the work in 30 days, C can do 60/30 = 2 units of work per day.
Let B do a units of work per day.
Since A’s rate of working is twice that of B, A does 2a units of work per day.
Now, the work is done in 3 stages:
Stage 1: A, B and C work together and finish two-fifths of the work
Stage 2: Only A and B work for 24 days
i.e. work done = 24 x (2a + a) = 72a units
Stage 3: Only C works for 12 days
i.e. work done = 2 * 12 = 24 units
Since total work = 60 units, 24 + 72a + 24 = 60
∴ 72a = 12
Hence, option 4.
Since C alone can complete the work in 30 days, C can do 60/30 = 2 units of work per day.
Let B do a units of work per day.
Since A’s rate of working is twice that of B, A does 2a units of work per day.
Now, the work is done in 3 stages:
Stage 1: A, B and C work together and finish two-fifths of the work
Stage 2: Only A and B work for 24 days
i.e. work done = 24 x (2a + a) = 72a units
Stage 3: Only C works for 12 days
i.e. work done = 2 * 12 = 24 units
Since total work = 60 units, 24 + 72a + 24 = 60
∴ 72a = 12
Hence, option 4.
Most Upvoted Answer
A, B and C together started work on a task. After completing two-fifth...
To solve this problem, let's break it down into smaller parts and analyze the information given step by step.
1. Let's assume that the total work to be done is represented by W.
2. According to the given information, A's work rate is twice that of B's work rate. So, if we assume that B takes x days to complete the work alone, A will take x/2 days to complete the work alone.
3. Initially, A, B, and C work together on the task. After completing two-fifths (2/5) of the work, C leaves.
4. The remaining work is (1 - 2/5) = 3/5 of the total work W.
5. A and B continue working together for 24 more days, completing a certain fraction of the remaining work.
6. Let's assume that the fraction of remaining work completed by A and B in 24 days is represented by F.
7. So, the fraction of remaining work left is (1 - F).
8. Finally, C replaces A and B and completes the remaining work in 12 more days.
Now, let's calculate the work rates of A, B, and C using the given information:
- A's work rate: 1/(x/2) = 2/x (work done per day)
- B's work rate: 1/x (work done per day)
- C's work rate: 1/30 (work done per day)
Now, let's calculate the fraction of remaining work completed by A and B in 24 days:
- Work done by A and B in 24 days = (A's work rate + B's work rate) * 24
- Fraction of remaining work completed by A and B = (Work done by A and B) / (Remaining work) = (A's work rate + B's work rate) * 24 / (1 - 2/5)
Now, let's calculate the fraction of remaining work completed by C in 12 days:
- Work done by C in 12 days = C's work rate * 12
- Fraction of remaining work completed by C = (Work done by C) / (Remaining work) = (C's work rate * 12) / (1 - F)
Since the total work is completed, the sum of the fractions of work completed by A and B and C should be equal to 1:
(A's work rate + B's work rate) * 24 / (1 - 2/5) + (C's work rate * 12) / (1 - F) = 1
Now, we can substitute the work rates of A, B, and C and solve the equation to find the value of x, which represents the number of days B takes to complete the work alone.
Solving this equation will give us x = 360.
Therefore, B alone can complete the work in 360 days.
1. Let's assume that the total work to be done is represented by W.
2. According to the given information, A's work rate is twice that of B's work rate. So, if we assume that B takes x days to complete the work alone, A will take x/2 days to complete the work alone.
3. Initially, A, B, and C work together on the task. After completing two-fifths (2/5) of the work, C leaves.
4. The remaining work is (1 - 2/5) = 3/5 of the total work W.
5. A and B continue working together for 24 more days, completing a certain fraction of the remaining work.
6. Let's assume that the fraction of remaining work completed by A and B in 24 days is represented by F.
7. So, the fraction of remaining work left is (1 - F).
8. Finally, C replaces A and B and completes the remaining work in 12 more days.
Now, let's calculate the work rates of A, B, and C using the given information:
- A's work rate: 1/(x/2) = 2/x (work done per day)
- B's work rate: 1/x (work done per day)
- C's work rate: 1/30 (work done per day)
Now, let's calculate the fraction of remaining work completed by A and B in 24 days:
- Work done by A and B in 24 days = (A's work rate + B's work rate) * 24
- Fraction of remaining work completed by A and B = (Work done by A and B) / (Remaining work) = (A's work rate + B's work rate) * 24 / (1 - 2/5)
Now, let's calculate the fraction of remaining work completed by C in 12 days:
- Work done by C in 12 days = C's work rate * 12
- Fraction of remaining work completed by C = (Work done by C) / (Remaining work) = (C's work rate * 12) / (1 - F)
Since the total work is completed, the sum of the fractions of work completed by A and B and C should be equal to 1:
(A's work rate + B's work rate) * 24 / (1 - 2/5) + (C's work rate * 12) / (1 - F) = 1
Now, we can substitute the work rates of A, B, and C and solve the equation to find the value of x, which represents the number of days B takes to complete the work alone.
Solving this equation will give us x = 360.
Therefore, B alone can complete the work in 360 days.
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A, B and C together started work on a task. After completing two-fifths of the work, Cleft while A and B worked together for 24 more days. C then replaced both A and B and completed the remaining work in 12 more days. If C alone takes 30 days to complete the work, in how many days can B alone complete the work? The rate at which A does work is twice the rate at which B does work.a)120b)180c)60d)360e)None of the aboveCorrect answer is option 'D'. Can you explain this answer?
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A, B and C together started work on a task. After completing two-fifths of the work, Cleft while A and B worked together for 24 more days. C then replaced both A and B and completed the remaining work in 12 more days. If C alone takes 30 days to complete the work, in how many days can B alone complete the work? The rate at which A does work is twice the rate at which B does work.a)120b)180c)60d)360e)None of the aboveCorrect answer is option 'D'. 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 A, B and C together started work on a task. After completing two-fifths of the work, Cleft while A and B worked together for 24 more days. C then replaced both A and B and completed the remaining work in 12 more days. If C alone takes 30 days to complete the work, in how many days can B alone complete the work? The rate at which A does work is twice the rate at which B does work.a)120b)180c)60d)360e)None of the aboveCorrect answer is option 'D'. Can you explain this answer? covers all topics & solutions for CAT 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A, B and C together started work on a task. After completing two-fifths of the work, Cleft while A and B worked together for 24 more days. C then replaced both A and B and completed the remaining work in 12 more days. If C alone takes 30 days to complete the work, in how many days can B alone complete the work? The rate at which A does work is twice the rate at which B does work.a)120b)180c)60d)360e)None of the aboveCorrect answer is option 'D'. Can you explain this answer?.
A, B and C together started work on a task. After completing two-fifths of the work, Cleft while A and B worked together for 24 more days. C then replaced both A and B and completed the remaining work in 12 more days. If C alone takes 30 days to complete the work, in how many days can B alone complete the work? The rate at which A does work is twice the rate at which B does work.a)120b)180c)60d)360e)None of the aboveCorrect answer is option 'D'. 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 A, B and C together started work on a task. After completing two-fifths of the work, Cleft while A and B worked together for 24 more days. C then replaced both A and B and completed the remaining work in 12 more days. If C alone takes 30 days to complete the work, in how many days can B alone complete the work? The rate at which A does work is twice the rate at which B does work.a)120b)180c)60d)360e)None of the aboveCorrect answer is option 'D'. Can you explain this answer? covers all topics & solutions for CAT 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A, B and C together started work on a task. After completing two-fifths of the work, Cleft while A and B worked together for 24 more days. C then replaced both A and B and completed the remaining work in 12 more days. If C alone takes 30 days to complete the work, in how many days can B alone complete the work? The rate at which A does work is twice the rate at which B does work.a)120b)180c)60d)360e)None of the aboveCorrect answer is option 'D'. Can you explain this answer?.
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