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A, B and C can do a job working alone in 50, 75 and 20 days respectively. They all work together for 4 days, then C quits. How many days will A and B take to finish the rest of the job?
- a)20
- b)30
- c)18
- d)24
Correct answer is option 'A'. Can you explain this answer?
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Verified Answer
A, B and C can do a job working alone in 50, 75 and 20 days respective...
Suppose unit work = 300 units (LCM of 50, 75 & 20)
∴ Work done by A in one day = 300/50 = 6
Work done by B in one day = 300/75 = 4
Work done by C in one day = 300/20 = 15
∴ Work done by (A + B + C) in 4 days = 4 × (6 + 4 + 15) = 100
C quits after 4 days.
∴ Remaining work after 4 days = 300 – 100 = 200 units
∴ Time taken by A and B together to complete 200 units = 200/(6 + 4) = 20 days
Most Upvoted Answer
A, B and C can do a job working alone in 50, 75 and 20 days respective...
Given information:
- A can complete the job alone in 50 days.
- B can complete the job alone in 75 days.
- C can complete the job alone in 20 days.
Working together for 4 days:
- In one day, A can complete 1/50 of the job.
- In one day, B can complete 1/75 of the job.
- In one day, C can complete 1/20 of the job.
- Working together, in one day, they can complete (1/50 + 1/75 + 1/20) of the job.
- Simplifying the above expression, we get (6/300 + 4/300 + 15/300) = 25/300 of the job in one day.
- In 4 days, they would have completed (25/300 * 4) = 100/300 = 1/3 of the job.
After C quits:
- A and B will be left to complete the remaining 2/3 of the job.
- Let's assume it takes them x days to complete the remaining job.
Calculating the number of days A and B take to finish the rest of the job:
- In one day, A can complete 1/50 of the job.
- In one day, B can complete 1/75 of the job.
- Together, in one day, A and B can complete (1/50 + 1/75) of the job.
- Simplifying the above expression, we get (3/150 + 2/150) = 5/150 of the job in one day.
- Since we assume it takes x days for A and B to complete the remaining 2/3 of the job, we can write the equation: (5/150) * x = 2/3.
- Multiplying both sides of the equation by 150, we get 5x = (2/3) * 150.
- Simplifying the right side of the equation, we get 5x = 100.
- Dividing both sides of the equation by 5, we get x = 20.
Therefore, A and B will take 20 days to finish the rest of the job after C quits. Hence, the correct answer is option A.
- A can complete the job alone in 50 days.
- B can complete the job alone in 75 days.
- C can complete the job alone in 20 days.
Working together for 4 days:
- In one day, A can complete 1/50 of the job.
- In one day, B can complete 1/75 of the job.
- In one day, C can complete 1/20 of the job.
- Working together, in one day, they can complete (1/50 + 1/75 + 1/20) of the job.
- Simplifying the above expression, we get (6/300 + 4/300 + 15/300) = 25/300 of the job in one day.
- In 4 days, they would have completed (25/300 * 4) = 100/300 = 1/3 of the job.
After C quits:
- A and B will be left to complete the remaining 2/3 of the job.
- Let's assume it takes them x days to complete the remaining job.
Calculating the number of days A and B take to finish the rest of the job:
- In one day, A can complete 1/50 of the job.
- In one day, B can complete 1/75 of the job.
- Together, in one day, A and B can complete (1/50 + 1/75) of the job.
- Simplifying the above expression, we get (3/150 + 2/150) = 5/150 of the job in one day.
- Since we assume it takes x days for A and B to complete the remaining 2/3 of the job, we can write the equation: (5/150) * x = 2/3.
- Multiplying both sides of the equation by 150, we get 5x = (2/3) * 150.
- Simplifying the right side of the equation, we get 5x = 100.
- Dividing both sides of the equation by 5, we get x = 20.
Therefore, A and B will take 20 days to finish the rest of the job after C quits. Hence, the correct answer is option A.
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A, B and C can do a job working alone in 50, 75 and 20 days respectively. They all work together for 4 days, then C quits. How many days will A and B take to finish the rest of the job?a)20b)30c)18d)24Correct answer is option 'A'. Can you explain this answer?
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