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Working 5 hours a day, A can complete a work in 8 days, and working 6 hours a day, B can complete the same work in 10 days. Working 8 hours a day, they can jointly complete the work in:
- a)3 days
- b)4 days
- c)4.5 days
- d)5.4 days
Correct answer is option 'A'. Can you explain this answer?
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Working 5 hours a day, A can complete a work in 8 days, and working 6...
Working 5 hours a day, A can complete the work in 8 days
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= 5 × 8
= 40 hours
Working 6 hours a day, B can complete the work in 10 days
= 6 × 10
= 60 hours
(A + B)'s 1 hour's work,
So, A and B can complete the work in 24 hours,
they require 3 days to complete the work.
Hence, the correct option is (A).
Most Upvoted Answer
Working 5 hours a day, A can complete a work in 8 days, and working 6...
To solve this problem, let's first find out the individual work rates of A and B.
Let's assume that the total work to be completed is represented by W.
Step 1: Calculate A's work rate
Working 5 hours a day, A can complete the work in 8 days. Therefore, A's work rate can be calculated as follows:
Work rate of A = W / (5 hours/day * 8 days)
= W / 40 hours
Step 2: Calculate B's work rate
Working 6 hours a day, B can complete the work in 10 days. Therefore, B's work rate can be calculated as follows:
Work rate of B = W / (6 hours/day * 10 days)
= W / 60 hours
Now, let's find out the combined work rate of A and B when they work together.
Step 3: Calculate the combined work rate
When A and B work together, their work rates will add up. So, the combined work rate can be calculated as follows:
Combined work rate = Work rate of A + Work rate of B
= W / 40 hours + W / 60 hours
Step 4: Find the time taken to complete the work when they work together
To find the time taken to complete the work when they work together, we need to find the reciprocal of the combined work rate.
Time taken = 1 / (Combined work rate)
= 1 / (W / 40 hours + W / 60 hours)
Simplifying this expression, we get:
Time taken = 1 / (3W / 120 hours)
= 120 hours / 3W
= 40 hours / W
Since the question asks for the time taken in days, we need to convert the time taken from hours to days.
Step 5: Convert hours to days
Since A and B are working together for 8 hours a day, the time taken in days can be calculated as follows:
Time taken = (40 hours / W) / 8 hours per day
= 5 days / W
Therefore, when A and B work together for 8 hours a day, they can complete the work in 5 days.
Hence, the correct answer is option A) 3 days.
Let's assume that the total work to be completed is represented by W.
Step 1: Calculate A's work rate
Working 5 hours a day, A can complete the work in 8 days. Therefore, A's work rate can be calculated as follows:
Work rate of A = W / (5 hours/day * 8 days)
= W / 40 hours
Step 2: Calculate B's work rate
Working 6 hours a day, B can complete the work in 10 days. Therefore, B's work rate can be calculated as follows:
Work rate of B = W / (6 hours/day * 10 days)
= W / 60 hours
Now, let's find out the combined work rate of A and B when they work together.
Step 3: Calculate the combined work rate
When A and B work together, their work rates will add up. So, the combined work rate can be calculated as follows:
Combined work rate = Work rate of A + Work rate of B
= W / 40 hours + W / 60 hours
Step 4: Find the time taken to complete the work when they work together
To find the time taken to complete the work when they work together, we need to find the reciprocal of the combined work rate.
Time taken = 1 / (Combined work rate)
= 1 / (W / 40 hours + W / 60 hours)
Simplifying this expression, we get:
Time taken = 1 / (3W / 120 hours)
= 120 hours / 3W
= 40 hours / W
Since the question asks for the time taken in days, we need to convert the time taken from hours to days.
Step 5: Convert hours to days
Since A and B are working together for 8 hours a day, the time taken in days can be calculated as follows:
Time taken = (40 hours / W) / 8 hours per day
= 5 days / W
Therefore, when A and B work together for 8 hours a day, they can complete the work in 5 days.
Hence, the correct answer is option A) 3 days.
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Working 5 hours a day, A can complete a work in 8 days, and working 6 hours a day, B can complete the same work in 10 days. Working 8 hours a day, they can jointly complete the work in:a)3 daysb)4 daysc)4.5 daysd)5.4 daysCorrect answer is option 'A'. Can you explain this answer?
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