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A can do a work in 32 days. P who is 60 percent more efficient than A. Find how much time they will take together to do the same work?
- a)150/13 days
- b)160/13 days
- c)170/3 days
- d)190/3 days
- e)None of these
Correct answer is option 'B'. Can you explain this answer?
Verified Answer
A can do a work in 32 days. P who is 60 percent more efficient than A....
A’s one day work = 1/32 so P one day work = (160/100)*1/32 = 1/20, so P will take 20 days to complete the work.
So Both A and P will take = (32*20)/52 = 160/13 days
So Both A and P will take = (32*20)/52 = 160/13 days
Most Upvoted Answer
A can do a work in 32 days. P who is 60 percent more efficient than A....
Let's assume that A can complete the work in 32 days. This means that A's efficiency is 1/32 of the work per day.
Now, let's find out P's efficiency. It is given that P is 60% more efficient than A. To calculate P's efficiency, we add 60% of A's efficiency to A's efficiency.
60% of A's efficiency = (60/100) * (1/32) = 3/160
P's efficiency = A's efficiency + 60% of A's efficiency = (1/32) + (3/160) = 5/160
So, P's efficiency is 5/160 of the work per day.
Let's calculate how much time P will take to complete the work alone.
P's efficiency = 5/160 of the work per day
Therefore, P will complete the work in 160/5 = 32 days.
Now, let's find out how much time A and P will take together to complete the work.
Let's assume that they will take 'x' days to complete the work together.
In one day, A completes 1/32 of the work, and P completes 1/32 of the work.
So, in 'x' days, A will complete x/32 of the work, and P will complete x/32 of the work.
Together, A and P complete (x/32) + (x/32) = 2x/32 of the work in 'x' days.
But we know that they complete the entire work together, so:
2x/32 = 1
Multiplying both sides by 32:
2x = 32
Dividing both sides by 2:
x = 16
Therefore, A and P will take 16 days together to complete the work.
The correct answer is option B) 160/13 days.
Now, let's find out P's efficiency. It is given that P is 60% more efficient than A. To calculate P's efficiency, we add 60% of A's efficiency to A's efficiency.
60% of A's efficiency = (60/100) * (1/32) = 3/160
P's efficiency = A's efficiency + 60% of A's efficiency = (1/32) + (3/160) = 5/160
So, P's efficiency is 5/160 of the work per day.
Let's calculate how much time P will take to complete the work alone.
P's efficiency = 5/160 of the work per day
Therefore, P will complete the work in 160/5 = 32 days.
Now, let's find out how much time A and P will take together to complete the work.
Let's assume that they will take 'x' days to complete the work together.
In one day, A completes 1/32 of the work, and P completes 1/32 of the work.
So, in 'x' days, A will complete x/32 of the work, and P will complete x/32 of the work.
Together, A and P complete (x/32) + (x/32) = 2x/32 of the work in 'x' days.
But we know that they complete the entire work together, so:
2x/32 = 1
Multiplying both sides by 32:
2x = 32
Dividing both sides by 2:
x = 16
Therefore, A and P will take 16 days together to complete the work.
The correct answer is option B) 160/13 days.
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