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A is 30% more efficient than B. How much time will they, working together, take to complete a job which A alone could have done in 23 days?
- a)11 days
- b)13 days
- c)20.176 days
- d)None of these
Correct answer is option 'B'. Can you explain this answer?
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Verified Answer
A is 30% more efficient than B. How much time will they, working toget...
Ratio of times taken by A and B = 100 : 130 = 10 : 13
Suppose B takes x days to do the work
Then, 10 : 13 :: 23 : x
⇒ x = ( 23 x 13/10 )
⇒ x = 299 10
A's 1 day's work = 1/23 :
B's 1 day's work = 10/299
(A + B)'s 1 day's work = ( 1/23 + 10/299 ) = 23/299 = 1/13
Therefore, A and B together can complete the work in 13 days
Suppose B takes x days to do the work
Then, 10 : 13 :: 23 : x
⇒ x = ( 23 x 13/10 )
⇒ x = 299 10
A's 1 day's work = 1/23 :
B's 1 day's work = 10/299
(A + B)'s 1 day's work = ( 1/23 + 10/299 ) = 23/299 = 1/13
Therefore, A and B together can complete the work in 13 days
Most Upvoted Answer
A is 30% more efficient than B. How much time will they, working toget...
To solve this problem, let's break it down into steps:
Step 1: Determine the time it takes for A to complete the job alone
Given that A alone could complete the job in 23 days, we can use this information to find A's efficiency. Let's assume that A's efficiency is 100 units (this is an arbitrary value to make calculations easier). Therefore, A can complete 100 units of work in 23 days.
Step 2: Determine the efficiency of B compared to A
Since A is 30% more efficient than B, B's efficiency can be calculated as follows:
B's efficiency = A's efficiency - (30% of A's efficiency)
B's efficiency = 100 - (30/100 * 100) = 100 - 30 = 70 units
Step 3: Determine the combined efficiency of A and B
To find the combined efficiency of A and B, we simply add their individual efficiencies:
Combined efficiency = A's efficiency + B's efficiency = 100 + 70 = 170 units
Step 4: Determine the time it takes for A and B to complete the job together
Since we know the combined efficiency of A and B is 170 units, we can now find the time it takes for them to complete the job together:
Combined time = Total work / Combined efficiency
Given that A alone could complete the job in 23 days, we know that the total work is 100 units. Therefore:
Combined time = 100 units / 170 units = 0.5882 days
Step 5: Convert the combined time to days and hours
Since 0.5882 days is less than 1 day, we can convert it to hours. There are 24 hours in a day, so:
Combined time = 0.5882 days * 24 hours/day = 14.1176 hours
Therefore, A and B working together will take approximately 14 hours to complete the job.
Step 1: Determine the time it takes for A to complete the job alone
Given that A alone could complete the job in 23 days, we can use this information to find A's efficiency. Let's assume that A's efficiency is 100 units (this is an arbitrary value to make calculations easier). Therefore, A can complete 100 units of work in 23 days.
Step 2: Determine the efficiency of B compared to A
Since A is 30% more efficient than B, B's efficiency can be calculated as follows:
B's efficiency = A's efficiency - (30% of A's efficiency)
B's efficiency = 100 - (30/100 * 100) = 100 - 30 = 70 units
Step 3: Determine the combined efficiency of A and B
To find the combined efficiency of A and B, we simply add their individual efficiencies:
Combined efficiency = A's efficiency + B's efficiency = 100 + 70 = 170 units
Step 4: Determine the time it takes for A and B to complete the job together
Since we know the combined efficiency of A and B is 170 units, we can now find the time it takes for them to complete the job together:
Combined time = Total work / Combined efficiency
Given that A alone could complete the job in 23 days, we know that the total work is 100 units. Therefore:
Combined time = 100 units / 170 units = 0.5882 days
Step 5: Convert the combined time to days and hours
Since 0.5882 days is less than 1 day, we can convert it to hours. There are 24 hours in a day, so:
Combined time = 0.5882 days * 24 hours/day = 14.1176 hours
Therefore, A and B working together will take approximately 14 hours to complete the job.
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A is 30% more efficient than B. How much time will they, working together, take to complete a job which A alone could have done in 23 days?a)11 daysb)13 daysc)20.176 daysd)None of theseCorrect answer is option 'B'. Can you explain this answer?
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