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Arijit and Brajesh, working together, can complete a task in 10 days, whereas Brajesh and Chandan can finish the same job in 15 days working together. If Arijit works for 5 days and Brajesh works for 8 days, it takes Chandan 9 days to complete the rest of the task. How many days will Chandan take to finish the same job alone?
- a)10 days
- b)20 days
- c)30 days
- d)None of the above
Correct answer is option 'B'. Can you explain this answer?
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Verified Answer
Arijit and Brajesh, working together, can complete a task in 10 days, ...
Let us assume that working alone Arijit completes the task in ‘a’ days, Brajesh completes in ‘b’ days and Chandan completes in ‘c’ days.
1/a + 1/b = 1/10 ...........(1)
1/b + 1/c = 1/15 ............ (2)
It is also given that:
5/a + 8/b + 9/c = 1
Or 5(1/a + 1/b) + 3(1/b + 1/c) + 6/c = 1
Using (1) and (2),
5/10 + 3/15 + 6/c = 1
Or 6/c = 1 - ½ - 1/5 = 3/10
Or c = 20.
Chandan can finish the task alone in 20 days.
1/a + 1/b = 1/10 ...........(1)
1/b + 1/c = 1/15 ............ (2)
It is also given that:
5/a + 8/b + 9/c = 1
Or 5(1/a + 1/b) + 3(1/b + 1/c) + 6/c = 1
Using (1) and (2),
5/10 + 3/15 + 6/c = 1
Or 6/c = 1 - ½ - 1/5 = 3/10
Or c = 20.
Chandan can finish the task alone in 20 days.
Most Upvoted Answer
Arijit and Brajesh, working together, can complete a task in 10 days, ...
Given:
Arijit and Brajesh can complete the task in 10 days working together.
Brajesh and Chandan can complete the task in 15 days working together.
Arijit works for 5 days and Brajesh works for 8 days.
Chandan completes the remaining task in 9 days.
To Find: The number of days Chandan will take to complete the task alone.
Solution:
Let the total work be W.
Let Arijit's efficiency be A, Brajesh's efficiency be B and Chandan's efficiency be C.
From the given information, we can form the following equations:
A + B = W/10 ...(1)
B + C = W/15 ...(2)
Arijit works for 5 days and Brajesh works for 8 days, so the work completed by them is:
5A + 8B = (5/10)W + (8/10)W = W ...(3)
Using equations (1) and (2), we can find B:
B = (W/15) - C ...(4)
Substituting equation (4) in equation (1), we get:
A + [(W/15) - C] = W/10
A - C = W/30 ...(5)
Chandan completes the remaining work in 9 days, so we can write:
9C = (7/10)W ...(6)
From equations (5) and (6), we can find C:
C = (7/90)W
Substituting this value of C in equation (4), we get:
B = W/45
From equation (2), we can find:
W/15 = B + C = W/45 + (7/90)W
W/15 = (4/45)W + (7/90)W
W/15 = (9/90)W
W = 150
Substituting the value of W in equation (6), we get:
9C = (7/10)(150)
C = 14
Therefore, Chandan will take 14 days to complete the task alone.
Hence, the correct answer is option (b) 20 days.
Arijit and Brajesh can complete the task in 10 days working together.
Brajesh and Chandan can complete the task in 15 days working together.
Arijit works for 5 days and Brajesh works for 8 days.
Chandan completes the remaining task in 9 days.
To Find: The number of days Chandan will take to complete the task alone.
Solution:
Let the total work be W.
Let Arijit's efficiency be A, Brajesh's efficiency be B and Chandan's efficiency be C.
From the given information, we can form the following equations:
A + B = W/10 ...(1)
B + C = W/15 ...(2)
Arijit works for 5 days and Brajesh works for 8 days, so the work completed by them is:
5A + 8B = (5/10)W + (8/10)W = W ...(3)
Using equations (1) and (2), we can find B:
B = (W/15) - C ...(4)
Substituting equation (4) in equation (1), we get:
A + [(W/15) - C] = W/10
A - C = W/30 ...(5)
Chandan completes the remaining work in 9 days, so we can write:
9C = (7/10)W ...(6)
From equations (5) and (6), we can find C:
C = (7/90)W
Substituting this value of C in equation (4), we get:
B = W/45
From equation (2), we can find:
W/15 = B + C = W/45 + (7/90)W
W/15 = (4/45)W + (7/90)W
W/15 = (9/90)W
W = 150
Substituting the value of W in equation (6), we get:
9C = (7/10)(150)
C = 14
Therefore, Chandan will take 14 days to complete the task alone.
Hence, the correct answer is option (b) 20 days.
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Arijit and Brajesh, working together, can complete a task in 10 days, whereas Brajesh and Chandan can finish the same job in 15 days working together. If Arijit works for 5 days and Brajesh works for 8 days, it takes Chandan 9 days to complete the rest of the task. How many days will Chandan take to finish the same job alone?a)10 daysb)20 daysc)30 daysd)None of the aboveCorrect answer is option 'B'. Can you explain this answer?
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Arijit and Brajesh, working together, can complete a task in 10 days, whereas Brajesh and Chandan can finish the same job in 15 days working together. If Arijit works for 5 days and Brajesh works for 8 days, it takes Chandan 9 days to complete the rest of the task. How many days will Chandan take to finish the same job alone?a)10 daysb)20 daysc)30 daysd)None of the aboveCorrect answer is option 'B'. Can you explain this answer? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about Arijit and Brajesh, working together, can complete a task in 10 days, whereas Brajesh and Chandan can finish the same job in 15 days working together. If Arijit works for 5 days and Brajesh works for 8 days, it takes Chandan 9 days to complete the rest of the task. How many days will Chandan take to finish the same job alone?a)10 daysb)20 daysc)30 daysd)None of the aboveCorrect answer is option 'B'. Can you explain this answer? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Arijit and Brajesh, working together, can complete a task in 10 days, whereas Brajesh and Chandan can finish the same job in 15 days working together. If Arijit works for 5 days and Brajesh works for 8 days, it takes Chandan 9 days to complete the rest of the task. How many days will Chandan take to finish the same job alone?a)10 daysb)20 daysc)30 daysd)None of the aboveCorrect answer is option 'B'. Can you explain this answer?.
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