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A and B together can do a works in 12 days. B and C together do it in 15 days. If A's efficiency is twice that of C, then the days required for B alone to finish the work is
- a)60
- b)30
- c)20
- d)15
Correct answer is option 'C'. Can you explain this answer?
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A and B together can do a works in 12 days. B and C together do it in ...
Given information:
- A and B together can do a work in 12 days.
- B and C together can do the same work in 15 days.
- Efficiency of A is twice that of C.
Let's assume that the total work is 60 units (LCM of 12 and 15).
- So, A and B together can do 5 units of work in a day (60/12 = 5).
- And, B and C together can do 4 units of work in a day (60/15 = 4).
Let's represent the efficiency of C as x units of work per day.
- So, the efficiency of A will be 2x units of work per day (as given).
- Therefore, the efficiency of B will be (5 - 2x) units of work per day (since A and B together can do 5 units of work in a day).
Now, let's apply the concept of work and efficiency to find the time taken by B alone to do the work.
- A and B together can do 2x + (5 - 2x) = 5 units of work in a day.
- Therefore, the efficiency of C will be x = 5/2 units of work per day.
- And, the efficiency of B will be (5 - 2x) = 5 - (5/2) = 5/2 units of work per day.
- So, B alone can do (5/2) units of work in a day.
- Therefore, B alone will take (60/(5/2)) = 24 days to finish the work.
Hence, the correct answer is option C (20 days).
- A and B together can do a work in 12 days.
- B and C together can do the same work in 15 days.
- Efficiency of A is twice that of C.
Let's assume that the total work is 60 units (LCM of 12 and 15).
- So, A and B together can do 5 units of work in a day (60/12 = 5).
- And, B and C together can do 4 units of work in a day (60/15 = 4).
Let's represent the efficiency of C as x units of work per day.
- So, the efficiency of A will be 2x units of work per day (as given).
- Therefore, the efficiency of B will be (5 - 2x) units of work per day (since A and B together can do 5 units of work in a day).
Now, let's apply the concept of work and efficiency to find the time taken by B alone to do the work.
- A and B together can do 2x + (5 - 2x) = 5 units of work in a day.
- Therefore, the efficiency of C will be x = 5/2 units of work per day.
- And, the efficiency of B will be (5 - 2x) = 5 - (5/2) = 5/2 units of work per day.
- So, B alone can do (5/2) units of work in a day.
- Therefore, B alone will take (60/(5/2)) = 24 days to finish the work.
Hence, the correct answer is option C (20 days).
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Community Answer
A and B together can do a works in 12 days. B and C together do it in ...
A and B will do in 1 day, 1/12 amount of work
B and C will do in 1 day, 1/15 amount of work
Hence adding up above two equations
A + 2B + C will do in 1 day, 9/60 amount of work
as it is mentioned A = 2C (i.e. efficiency of A is twice of C)
So 2C + 2B + C will do in 1 day 9/60 amount of work
or 2(B+C) + C = 9/60
or C = 1/60 (as B + C = 1/15)
So B alone will do work in 20 days.
B and C will do in 1 day, 1/15 amount of work
Hence adding up above two equations
A + 2B + C will do in 1 day, 9/60 amount of work
as it is mentioned A = 2C (i.e. efficiency of A is twice of C)
So 2C + 2B + C will do in 1 day 9/60 amount of work
or 2(B+C) + C = 9/60
or C = 1/60 (as B + C = 1/15)
So B alone will do work in 20 days.
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A and B together can do a works in 12 days. B and C together do it in 15 days. If As efficiency is twice that of C, then the days required for B alone to finish the work isa)60b)30c)20d)15Correct answer is option 'C'. Can you explain this answer?
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