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A and B together can do a piece of work in 50 days. If A is 40% less efficient than B, in how many days can A working alone complete 60% of the work?
- a)70
- b)110
- c)80
- d)105
Correct answer is option 'C'. Can you explain this answer?
Most Upvoted Answer
A and B together can do a piece of work in 50 days. If A is 40% less e...
Given:
A and B together can do a piece of work in 50 days.
A is 40% less efficient than B
Concept used:
Total work = Efficiency of the workers × time taken by them
Calculation:
Let the efficiency of B be 5a
So, efficiency of A = 5a × 60%
⇒ 3a
So, total efficiency of them = 8a
Total work = 8a × 50
⇒ 400a
Now,
60% of the work = 400a × 60%
⇒ 240a
Now,
Required time = 240a/3a
⇒ 80 days
∴ A can complete 60% of the work working alone in 80 days.
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A and B together can do a piece of work in 50 days. If A is 40% less e...
To solve this problem, let's assume that B can complete the work in x days.
Efficiency of A = 100% - 40% = 60% of B.
Let's calculate the efficiency of A and B:
Efficiency of A = 60% of B = (60/100) * B = 0.6B
Efficiency of B = B
Now, let's calculate the work done by A and B in one day:
Work done by A in one day = Efficiency of A * 1 day = 0.6B * 1 = 0.6B
Work done by B in one day = Efficiency of B * 1 day = B * 1 = B
Working together, A and B can complete the work in 50 days. So, in one day, they can complete 1/50th of the work.
Work done by A and B together in one day = 1/50th of the work
Adding the work done by A and B in one day, we get:
0.6B + B = 1/50
Simplifying the equation, we have:
1.6B = 1/50
Dividing both sides by 1.6, we get:
B = 1/50 * 1/1.6
B = 1/80
So, B can complete 1/80th of the work in one day.
Now, let's calculate the number of days it takes for A to complete 60% of the work:
Work done by A in one day = 0.6B
Substituting the value of B, we have:
Work done by A in one day = 0.6 * 1/80 = 1/133.33
To complete 60% of the work, A would require:
(60/100) * (1/133.33) = 1/222.22
So, A working alone can complete 1/222.22 of the work in one day.
To find the number of days required to complete 60% of the work, we divide 1 by 1/222.22:
1 / (1/222.22) = 222.22
Therefore, A working alone can complete 60% of the work in approximately 222.22 days.
However, none of the given options match this answer. So, it seems that there may be an error in the question or options provided.
Efficiency of A = 100% - 40% = 60% of B.
Let's calculate the efficiency of A and B:
Efficiency of A = 60% of B = (60/100) * B = 0.6B
Efficiency of B = B
Now, let's calculate the work done by A and B in one day:
Work done by A in one day = Efficiency of A * 1 day = 0.6B * 1 = 0.6B
Work done by B in one day = Efficiency of B * 1 day = B * 1 = B
Working together, A and B can complete the work in 50 days. So, in one day, they can complete 1/50th of the work.
Work done by A and B together in one day = 1/50th of the work
Adding the work done by A and B in one day, we get:
0.6B + B = 1/50
Simplifying the equation, we have:
1.6B = 1/50
Dividing both sides by 1.6, we get:
B = 1/50 * 1/1.6
B = 1/80
So, B can complete 1/80th of the work in one day.
Now, let's calculate the number of days it takes for A to complete 60% of the work:
Work done by A in one day = 0.6B
Substituting the value of B, we have:
Work done by A in one day = 0.6 * 1/80 = 1/133.33
To complete 60% of the work, A would require:
(60/100) * (1/133.33) = 1/222.22
So, A working alone can complete 1/222.22 of the work in one day.
To find the number of days required to complete 60% of the work, we divide 1 by 1/222.22:
1 / (1/222.22) = 222.22
Therefore, A working alone can complete 60% of the work in approximately 222.22 days.
However, none of the given options match this answer. So, it seems that there may be an error in the question or options provided.
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A and B together can do a piece of work in 50 days. If A is 40% less efficient than B, in how many days can Aworking alone complete 60% of the work?a)70b)110c)80d)105Correct answer is option 'C'. Can you explain this answer?
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