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A and B can do a job together in 12 days. A is 2 times as efficient as B. In how many days can B alone complete the work?
- a)18 days
- b)9 days
- c)36 days
- d)12 days
Correct answer is option 'C'. Can you explain this answer?
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Problem:
A and B can do a job together in 12 days. A is 2 times as efficient as B. In how many days can B alone complete the work?
Solution:
To solve this problem, we can use the concept of work efficiency and the formula:
Work Efficiency = Work / Time
Let's assume that B's work efficiency is "x" units per day. Since A is 2 times as efficient as B, A's work efficiency would be "2x" units per day.
Step 1: Calculate the combined work efficiency of A and B when working together.
The combined work efficiency of A and B is the sum of their individual work efficiencies:
Combined work efficiency = A's work efficiency + B's work efficiency
= 2x + x
= 3x units per day
Step 2: Calculate the time required for A and B to complete the job together.
We are given that A and B can complete the job together in 12 days. Therefore, using the formula for work efficiency:
Combined work efficiency = Work / Time
We can substitute the values:
3x = 1 (since they complete the job together)
12
Simplifying the equation, we get:
36x = 1
Step 3: Calculate the time required for B to complete the job alone.
Since B's work efficiency is "x" units per day, we can use the formula for work efficiency:
B's work efficiency = Work / Time
Substituting the values:
x = 1 (since B completes the job alone)
36
Simplifying the equation, we get:
x = 36
Therefore, B can complete the job alone in 36 days.
Conclusion: B alone can complete the work in 36 days.
A and B can do a job together in 12 days. A is 2 times as efficient as B. In how many days can B alone complete the work?
Solution:
To solve this problem, we can use the concept of work efficiency and the formula:
Work Efficiency = Work / Time
Let's assume that B's work efficiency is "x" units per day. Since A is 2 times as efficient as B, A's work efficiency would be "2x" units per day.
Step 1: Calculate the combined work efficiency of A and B when working together.
The combined work efficiency of A and B is the sum of their individual work efficiencies:
Combined work efficiency = A's work efficiency + B's work efficiency
= 2x + x
= 3x units per day
Step 2: Calculate the time required for A and B to complete the job together.
We are given that A and B can complete the job together in 12 days. Therefore, using the formula for work efficiency:
Combined work efficiency = Work / Time
We can substitute the values:
3x = 1 (since they complete the job together)
12
Simplifying the equation, we get:
36x = 1
Step 3: Calculate the time required for B to complete the job alone.
Since B's work efficiency is "x" units per day, we can use the formula for work efficiency:
B's work efficiency = Work / Time
Substituting the values:
x = 1 (since B completes the job alone)
36
Simplifying the equation, we get:
x = 36
Therefore, B can complete the job alone in 36 days.
Conclusion: B alone can complete the work in 36 days.
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A and B can do a job together in 12 days. A is 2 times as efficient as B. In how many days can B alone complete the work?a)18 daysb)9 daysc)36 daysd)12 daysCorrect answer is option 'C'. Can you explain this answer?
Question Description
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