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A is twice as efficient as B and B is twice as efficient as C. If A, B and C work together, a piece of work will be completed in 12 days. A and B work together for 8 days and thereafter, A is replaced by C.
How many more days are required to complete the work?
- a)8 days
- b)10 days
- c)12 days
- d)15 days
- e)16 days
Correct answer is option 'C'. Can you explain this answer?
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Verified Answer
A is twice as efficient as B and B is twice as efficient as C. If A, B...
Assume, C can do x work in 1 day; B can do 2x work in 1 day; and A can do 4x work in 1 day.
Total work = 12(x + 2x + 4x) = 84x
A and B work for 8 days, 8(2x + 4x) = 48x will be completed.
B and C can do 3x work in 1 day.
So, the remaining 36x can be completed in 12 days.
Total work = 12(x + 2x + 4x) = 84x
A and B work for 8 days, 8(2x + 4x) = 48x will be completed.
B and C can do 3x work in 1 day.
So, the remaining 36x can be completed in 12 days.
Most Upvoted Answer
A is twice as efficient as B and B is twice as efficient as C. If A, B...
Let's assume that the efficiency of C is x units per day.
Efficiency of B = 2x units per day
Efficiency of A = 4x units per day
Given that A, B, and C complete the work in 12 days when working together, we can set up the following equation:
(4x + 2x + x) * 12 = 1
(7x) * 12 = 1
84x = 1
x = 1/84
So, the efficiency of C is 1/84 units per day.
Now, let's calculate the work done by A and B in 8 days when working together.
Work done by A and B in 8 days = (4x + 2x) * 8 = 6x * 8 = 48x
The remaining work to be done after 8 days = 1 - 48x
Now, C replaces A and works alone to complete the remaining work.
The time taken by C to complete the remaining work = (1 - 48x) / x
We know that x = 1/84, so substituting the value of x, we get:
Time taken by C to complete the remaining work = (1 - 48 * (1/84)) / (1/84)
= (1 - (48/84)) * (84/1)
= (36/84) * 84
= 36
Therefore, it will take C 36 more days to complete the remaining work.
However, we need to consider the 8 days when A and B were working together.
Total time taken to complete the work = 8 days + 36 days = 44 days
Therefore, the correct answer is option C) 12 days.
Efficiency of B = 2x units per day
Efficiency of A = 4x units per day
Given that A, B, and C complete the work in 12 days when working together, we can set up the following equation:
(4x + 2x + x) * 12 = 1
(7x) * 12 = 1
84x = 1
x = 1/84
So, the efficiency of C is 1/84 units per day.
Now, let's calculate the work done by A and B in 8 days when working together.
Work done by A and B in 8 days = (4x + 2x) * 8 = 6x * 8 = 48x
The remaining work to be done after 8 days = 1 - 48x
Now, C replaces A and works alone to complete the remaining work.
The time taken by C to complete the remaining work = (1 - 48x) / x
We know that x = 1/84, so substituting the value of x, we get:
Time taken by C to complete the remaining work = (1 - 48 * (1/84)) / (1/84)
= (1 - (48/84)) * (84/1)
= (36/84) * 84
= 36
Therefore, it will take C 36 more days to complete the remaining work.
However, we need to consider the 8 days when A and B were working together.
Total time taken to complete the work = 8 days + 36 days = 44 days
Therefore, the correct answer is option C) 12 days.
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