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Two workers A and B can construct a wall in 10 hours and 20 hours respectively and a third worker C can destroy the same wall in 5 hours. A and B start constructing the wall, after 6 hours C joins them. After what time the wall will cease to exist?
- a)16 hours
- b)27 hours
- c)18 hours
- d)9 hours
Correct answer is option 'C'. Can you explain this answer?
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Verified Answer
Two workers A and B can construct a wall in 10 hours and 20 hours resp...
⇒ Let the total amount of work done in constructing a wall be 20 units (L.C.M of 5, 10, and 20)
Hence, work done by A in one hour = 20/10 = 2 units
Work done by B in one hour = 20/20 = 1 unit
Work done by C in one hour = -20/5 = -4 units
Work done by B in one hour = 20/20 = 1 unit
Work done by C in one hour = -20/5 = -4 units
⇒ Now, when A and B work together, work done by them in one hour is 2 + 1 = 3 units
They together work for 6 hours, therefore work done in 6 hours = 3 × 6 = 18 units
After 6 hours C joins them, work done by A, B and C in one hour = 2 + 1 - 4 = -1 unit
Time taken to nullify 27 units of work will be x hours,
⇒ 18 + x(-1) = 0
⇒ x = 18 hours
⇒ 18 + x(-1) = 0
⇒ x = 18 hours
Most Upvoted Answer
Two workers A and B can construct a wall in 10 hours and 20 hours resp...
⇒ Let the total amount of work done in constructing a wall be 20 units (L.C.M of 5, 10, and 20)
Hence, work done by A in one hour = 20/10 = 2 units
Work done by B in one hour = 20/20 = 1 unit
Work done by C in one hour = -20/5 = -4 units
Work done by B in one hour = 20/20 = 1 unit
Work done by C in one hour = -20/5 = -4 units
⇒ Now, when A and B work together, work done by them in one hour is 2 + 1 = 3 units
They together work for 6 hours, therefore work done in 6 hours = 3 × 6 = 18 units
After 6 hours C joins them, work done by A, B and C in one hour = 2 + 1 - 4 = -1 unit
Time taken to nullify 27 units of work will be x hours,
⇒ 18 + x(-1) = 0
⇒ x = 18 hours
⇒ 18 + x(-1) = 0
⇒ x = 18 hours
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Two workers A and B can construct a wall in 10 hours and 20 hours respectively and a third worker C can destroy the same wall in 5 hours. A and B start constructing the wall, after 6 hours C joins them. After what time the wall will cease to exist?a)16 hoursb)27 hoursc)18 hoursd)9 hoursCorrect answer is option 'C'. Can you explain this answer?
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