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A, B and C together can finish a piece of work in 12 days. A and C together work twice as much as B. A and B together work thrice as much as C. In what time will C finish the job alone?
- a)36 days
- b)48 days
- c)28 days
- d)32 days
Correct answer is option 'B'. Can you explain this answer?
Most Upvoted Answer
A, B and C together can finish a piece of work in 12 days. A and C tog...
Since A and C together work twice as much as B
A + C = 2B ... (1)
And A and B together work thrice as much as C
A + B = 3C ... (2)
Equation (1) - equation (2) gives
C - B = 2B - 3C
Or 3B = 4C
Or B = (4/3)C
Substituting this relation in equation (1), we get
A = (5/3)C
A + B + C = (5/3)C + (4/3)C + C = 4C
This means that 4C can complete the work in 12 days or C can complete in 12 x 4 = 48 days.
A + C = 2B ... (1)
And A and B together work thrice as much as C
A + B = 3C ... (2)
Equation (1) - equation (2) gives
C - B = 2B - 3C
Or 3B = 4C
Or B = (4/3)C
Substituting this relation in equation (1), we get
A = (5/3)C
A + B + C = (5/3)C + (4/3)C + C = 4C
This means that 4C can complete the work in 12 days or C can complete in 12 x 4 = 48 days.
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Community Answer
A, B and C together can finish a piece of work in 12 days. A and C tog...
Let's assume that the work done by A, B, and C in one day is represented by the variables a, b, and c respectively.
According to the given information:
- A, B, and C together can finish a piece of work in 12 days.
This implies that their combined daily work is equal to 1/12th of the total work. Therefore, we have the equation: a + b + c = 1/12.
- A and C together work twice as much as B.
This means that their combined daily work is equal to twice the work done by B. So, we have the equation: a + c = 2b.
- A and B together work thrice as much as C.
This implies that their combined daily work is equal to three times the work done by C. So, we have the equation: a + b = 3c.
We now have a system of three equations with three variables. We can solve this system to find the values of a, b, and c.
Solving the system of equations:
From the equation a + c = 2b, we can rewrite it as a = 2b - c.
Substituting this value of a in the equation a + b = 3c, we get:
2b - c + b = 3c
3b = 4c
b = (4/3)c
Substituting the value of b in the equation a + b + c = 1/12, we get:
a + (4/3)c + c = 1/12
a + (7/3)c = 1/12
Since a + b + c = 1/12, we can substitute the value of a + c = 2b in this equation:
2b + b = 1/12
3b = 1/12
b = 1/36
Substituting the value of b = (4/3)c in this equation, we get:
(4/3)c = 1/36
c = 1/36 * 3/4
c = 1/48
Therefore, C can finish the job alone in 48 days.
Hence, option B is the correct answer.
According to the given information:
- A, B, and C together can finish a piece of work in 12 days.
This implies that their combined daily work is equal to 1/12th of the total work. Therefore, we have the equation: a + b + c = 1/12.
- A and C together work twice as much as B.
This means that their combined daily work is equal to twice the work done by B. So, we have the equation: a + c = 2b.
- A and B together work thrice as much as C.
This implies that their combined daily work is equal to three times the work done by C. So, we have the equation: a + b = 3c.
We now have a system of three equations with three variables. We can solve this system to find the values of a, b, and c.
Solving the system of equations:
From the equation a + c = 2b, we can rewrite it as a = 2b - c.
Substituting this value of a in the equation a + b = 3c, we get:
2b - c + b = 3c
3b = 4c
b = (4/3)c
Substituting the value of b in the equation a + b + c = 1/12, we get:
a + (4/3)c + c = 1/12
a + (7/3)c = 1/12
Since a + b + c = 1/12, we can substitute the value of a + c = 2b in this equation:
2b + b = 1/12
3b = 1/12
b = 1/36
Substituting the value of b = (4/3)c in this equation, we get:
(4/3)c = 1/36
c = 1/36 * 3/4
c = 1/48
Therefore, C can finish the job alone in 48 days.
Hence, option B is the correct answer.
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A, B and C together can finish a piece of work in 12 days. A and C together work twice as much as B. A and B together work thrice as much as C. In what time will C finish the job alone?a)36 daysb)48 daysc)28 daysd)32 daysCorrect answer is option 'B'. Can you explain this answer? for CAT 2025 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 can finish a piece of work in 12 days. A and C together work twice as much as B. A and B together work thrice as much as C. In what time will C finish the job alone?a)36 daysb)48 daysc)28 daysd)32 daysCorrect answer is option 'B'. Can you explain this answer? covers all topics & solutions for CAT 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A, B and C together can finish a piece of work in 12 days. A and C together work twice as much as B. A and B together work thrice as much as C. In what time will C finish the job alone?a)36 daysb)48 daysc)28 daysd)32 daysCorrect answer is option 'B'. Can you explain this answer?.
A, B and C together can finish a piece of work in 12 days. A and C together work twice as much as B. A and B together work thrice as much as C. In what time will C finish the job alone?a)36 daysb)48 daysc)28 daysd)32 daysCorrect answer is option 'B'. Can you explain this answer? for CAT 2025 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 can finish a piece of work in 12 days. A and C together work twice as much as B. A and B together work thrice as much as C. In what time will C finish the job alone?a)36 daysb)48 daysc)28 daysd)32 daysCorrect answer is option 'B'. Can you explain this answer? covers all topics & solutions for CAT 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A, B and C together can finish a piece of work in 12 days. A and C together work twice as much as B. A and B together work thrice as much as C. In what time will C finish the job alone?a)36 daysb)48 daysc)28 daysd)32 daysCorrect answer is option 'B'. Can you explain this answer?.
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