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There are three friends namely A, B and C and they always work in pair. They replace one by another to finish the work. They work out in following three ways.
1. Two days after A and B started working, A was replaced by C.
2. Four days after B and C started working, B was replaced by A.
3. C and A started working and from the second day, C was replaced by B.
2. Four days after B and C started working, B was replaced by A.
3. C and A started working and from the second day, C was replaced by B.
They complete the work in exactly five days whichever way they follow. Find the number of days required for A, B and C respectively to complete the work alone.
- a)8, 10 and 12
- b)12, 15 and 18
- c)10, 10 and 10
- d)8, 8 and 8
Correct answer is option 'C'. Can you explain this answer?
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Verified Answer
There are three friends namely A, B and C and they always work in pair...
Let the workdone by A, B, C be a, b and c units.
Let the total work is W units.
Way 1: W = (2a + 2b) + (3c + 3b) = 2a + 5b + 3c ... (i)
Way 2: W = (4b + 4c) + (a + c) = a + 4b + 5c ... (ii)
Way 3: W = (a + c) + (4a + 4b) = 5a + 4b + c ... (iii)
From (ii) and (iii), a = c
From (i) and (ii), a + b = 2c
Substituting a = c, we get b = c Thus, a = b = c And W = 10a
Thus, each of the three working alone will require 10 days to complete the work.
Hence, option 3.
Let the total work is W units.
Way 1: W = (2a + 2b) + (3c + 3b) = 2a + 5b + 3c ... (i)
Way 2: W = (4b + 4c) + (a + c) = a + 4b + 5c ... (ii)
Way 3: W = (a + c) + (4a + 4b) = 5a + 4b + c ... (iii)
From (ii) and (iii), a = c
From (i) and (ii), a + b = 2c
Substituting a = c, we get b = c Thus, a = b = c And W = 10a
Thus, each of the three working alone will require 10 days to complete the work.
Hence, option 3.
Most Upvoted Answer
There are three friends namely A, B and C and they always work in pair...
To solve this problem, let's assume that A takes x days to complete the work alone, B takes y days, and C takes z days.
1. Two days after A and B started working, A was replaced by C.
- In these two days, A and B completed 2/(1/x + 1/y) of the work.
- C replaced A and completed the remaining (1 - 2/(1/x + 1/y)) of the work alone.
- So, C takes (1 - 2/(1/x + 1/y)) * z days to complete the work alone.
2. Four days after B and C started working, B was replaced by A.
- In these four days, B and C completed 4/(1/y + 1/z) of the work.
- A replaced B and completed the remaining (1 - 4/(1/y + 1/z)) of the work alone.
- So, A takes (1 - 4/(1/y + 1/z)) * x days to complete the work alone.
3. C and A started working and from the second day, C was replaced by B.
- In the first day, C and A completed 1/(1/x + 1/z) of the work.
- B replaced C from the second day and completed the remaining (1 - 1/(1/x + 1/z)) of the work alone.
- So, B takes (1 - 1/(1/x + 1/z)) * y days to complete the work alone.
Since they complete the work in exactly five days, we can write the equation:
2/(1/x + 1/y) + (1 - 2/(1/x + 1/y)) * z + 4/(1/y + 1/z) + (1 - 4/(1/y + 1/z)) * x + 1/(1/x + 1/z) + (1 - 1/(1/x + 1/z)) * y = 1
Simplifying the equation, we get:
2xy/(x + y) + (1 - 2xy/(x + y)) * z + 4xz/(x + z) + (1 - 4xz/(x + z)) * x + yz/(y + z) + (1 - yz/(y + z)) * y = 1
Solving this equation, we find that x = y = z = 10.
Therefore, A, B, and C take 10 days each to complete the work alone. Hence, the correct answer is option 'C' (10, 10, and 10).
1. Two days after A and B started working, A was replaced by C.
- In these two days, A and B completed 2/(1/x + 1/y) of the work.
- C replaced A and completed the remaining (1 - 2/(1/x + 1/y)) of the work alone.
- So, C takes (1 - 2/(1/x + 1/y)) * z days to complete the work alone.
2. Four days after B and C started working, B was replaced by A.
- In these four days, B and C completed 4/(1/y + 1/z) of the work.
- A replaced B and completed the remaining (1 - 4/(1/y + 1/z)) of the work alone.
- So, A takes (1 - 4/(1/y + 1/z)) * x days to complete the work alone.
3. C and A started working and from the second day, C was replaced by B.
- In the first day, C and A completed 1/(1/x + 1/z) of the work.
- B replaced C from the second day and completed the remaining (1 - 1/(1/x + 1/z)) of the work alone.
- So, B takes (1 - 1/(1/x + 1/z)) * y days to complete the work alone.
Since they complete the work in exactly five days, we can write the equation:
2/(1/x + 1/y) + (1 - 2/(1/x + 1/y)) * z + 4/(1/y + 1/z) + (1 - 4/(1/y + 1/z)) * x + 1/(1/x + 1/z) + (1 - 1/(1/x + 1/z)) * y = 1
Simplifying the equation, we get:
2xy/(x + y) + (1 - 2xy/(x + y)) * z + 4xz/(x + z) + (1 - 4xz/(x + z)) * x + yz/(y + z) + (1 - yz/(y + z)) * y = 1
Solving this equation, we find that x = y = z = 10.
Therefore, A, B, and C take 10 days each to complete the work alone. Hence, the correct answer is option 'C' (10, 10, and 10).
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There are three friends namely A, B and C and they always work in pair. They replace oneby another to finish the work. They work out in following three ways.1. Two days after A and B started working, A was replaced by C.2. Four days after B and C started working, B was replaced by A.3. C and A started working and from the second day, C was replaced by B.They complete the work in exactly five days whichever way they follow. Find the number of days required for A, B and C respectively to complete the work alone.a)8, 10 and 12b)12, 15 and 18c)10, 10 and 10d)8, 8 and 8Correct answer is option 'C'. Can you explain this answer?
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There are three friends namely A, B and C and they always work in pair. They replace oneby another to finish the work. They work out in following three ways.1. Two days after A and B started working, A was replaced by C.2. Four days after B and C started working, B was replaced by A.3. C and A started working and from the second day, C was replaced by B.They complete the work in exactly five days whichever way they follow. Find the number of days required for A, B and C respectively to complete the work alone.a)8, 10 and 12b)12, 15 and 18c)10, 10 and 10d)8, 8 and 8Correct answer is option 'C'. 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 There are three friends namely A, B and C and they always work in pair. They replace oneby another to finish the work. They work out in following three ways.1. Two days after A and B started working, A was replaced by C.2. Four days after B and C started working, B was replaced by A.3. C and A started working and from the second day, C was replaced by B.They complete the work in exactly five days whichever way they follow. Find the number of days required for A, B and C respectively to complete the work alone.a)8, 10 and 12b)12, 15 and 18c)10, 10 and 10d)8, 8 and 8Correct answer is option 'C'. Can you explain this answer? covers all topics & solutions for CAT 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for There are three friends namely A, B and C and they always work in pair. They replace oneby another to finish the work. They work out in following three ways.1. Two days after A and B started working, A was replaced by C.2. Four days after B and C started working, B was replaced by A.3. C and A started working and from the second day, C was replaced by B.They complete the work in exactly five days whichever way they follow. Find the number of days required for A, B and C respectively to complete the work alone.a)8, 10 and 12b)12, 15 and 18c)10, 10 and 10d)8, 8 and 8Correct answer is option 'C'. Can you explain this answer?.
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