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At their usual efficiency levels, A and B together finish a task in 12 days. If A had worked half as efficiently as she usually does, and B had worked thrice as efficiently as he usually does, the task would have been completed in 9 days. How many days would A take to finish the task if she works alone at her usual efficiency?
- a)36
- b)24
- c)18
- d)12
Correct answer is option 'C'. Can you explain this answer?
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Verified Answer
At their usual efficiency levels, A and B together finish a task in 1...
Assuming A completes a units of work in a day and B completes B units of work in a day and the total work = 1 unit
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Hence, 12(a+b)=1……(1)
Also, 9(a/2+3b)=1
Using both equations, we get, 12(a+b)= 9(a/2+3b)
=> 4a+4b= 3a/2 +9b
5a/2 =5b
=> a=2b
Substituting the value of b in equation (1),
12(3a/2) = 1
=>a=1/18
Hence, the number of days required = 1/(1/18)=18
Most Upvoted Answer
At their usual efficiency levels, A and B together finish a task in 1...
Given:
Efficiency of A and B together = 1/12
Let's assume A's usual efficiency = a and B's usual efficiency = b
To find:
How long would A take to finish the task if she works alone at her usual efficiency?
Solution:
Let's find the total work:
A and B together can finish the task in 12 days, so their one day work = 1/12
Let's assume the total work is W
So, A and B together can finish W work in 12 days
A and B's one day work together = 1/12
A's one day work = a
B's one day work = b
So, a + b = 1/12 ----(1)
Now given, if A had worked half as efficiently as she usually does, and B had worked thrice as efficiently as he usually does, the task would have been completed in 9 days.
So, A's new efficiency = a/2
B's new efficiency = 3b
A's one day work with new efficiency = a/2
B's one day work with new efficiency = 3b
Together, their one day work with new efficiency = a/2 + 3b
Together, they can finish W work in 9 days
So, their one day work with new efficiency = W/9
a/2 + 3b = W/9 ----(2)
Solving equations (1) and (2) to find a and b:
a + b = 1/12
a/2 + 3b = W/9
Multiplying equation (1) by 3 and subtracting from equation (2):
a/2 + 3b - 3a - 3b = W/9 - 1/4
-5a/2 = W/9 - 1/4
a = (1/4 - W/9) * (-2/5)
Substituting value of a in equation (1):
(1/4 - W/9) * (-2/5) + b = 1/12
b = (1/12 + 2/45 - W/45) * 5
Now, we know a and b, so we can find how long A would take to finish the task alone at her usual efficiency:
A's one day work = a
Total work = W
So, A alone can finish W work in 'x' days
a = 1/x
1/x = (1/4 - W/9) * (-2/5)
x = 18
Therefore, A alone can finish the task in 18 days.
Hence, option (c) is the correct answer.
Efficiency of A and B together = 1/12
Let's assume A's usual efficiency = a and B's usual efficiency = b
To find:
How long would A take to finish the task if she works alone at her usual efficiency?
Solution:
Let's find the total work:
A and B together can finish the task in 12 days, so their one day work = 1/12
Let's assume the total work is W
So, A and B together can finish W work in 12 days
A and B's one day work together = 1/12
A's one day work = a
B's one day work = b
So, a + b = 1/12 ----(1)
Now given, if A had worked half as efficiently as she usually does, and B had worked thrice as efficiently as he usually does, the task would have been completed in 9 days.
So, A's new efficiency = a/2
B's new efficiency = 3b
A's one day work with new efficiency = a/2
B's one day work with new efficiency = 3b
Together, their one day work with new efficiency = a/2 + 3b
Together, they can finish W work in 9 days
So, their one day work with new efficiency = W/9
a/2 + 3b = W/9 ----(2)
Solving equations (1) and (2) to find a and b:
a + b = 1/12
a/2 + 3b = W/9
Multiplying equation (1) by 3 and subtracting from equation (2):
a/2 + 3b - 3a - 3b = W/9 - 1/4
-5a/2 = W/9 - 1/4
a = (1/4 - W/9) * (-2/5)
Substituting value of a in equation (1):
(1/4 - W/9) * (-2/5) + b = 1/12
b = (1/12 + 2/45 - W/45) * 5
Now, we know a and b, so we can find how long A would take to finish the task alone at her usual efficiency:
A's one day work = a
Total work = W
So, A alone can finish W work in 'x' days
a = 1/x
1/x = (1/4 - W/9) * (-2/5)
x = 18
Therefore, A alone can finish the task in 18 days.
Hence, option (c) is the correct answer.
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At their usual efficiency levels, A and B together finish a task in 12 days. If A had worked half as efficiently as she usually does, and B had worked thrice as efficiently as he usually does, the task would have been completed in 9 days. How many days would A take to finish the task if she works alone at her usual efficiency?a) 36b) 24c) 18d) 12Correct answer is option 'C'. Can you explain this answer?
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At their usual efficiency levels, A and B together finish a task in 12 days. If A had worked half as efficiently as she usually does, and B had worked thrice as efficiently as he usually does, the task would have been completed in 9 days. How many days would A take to finish the task if she works alone at her usual efficiency?a) 36b) 24c) 18d) 12Correct answer is option 'C'. Can you explain this answer? for SSC 2024 is part of SSC preparation. The Question and answers have been prepared according to the SSC exam syllabus. Information about At their usual efficiency levels, A and B together finish a task in 12 days. If A had worked half as efficiently as she usually does, and B had worked thrice as efficiently as he usually does, the task would have been completed in 9 days. How many days would A take to finish the task if she works alone at her usual efficiency?a) 36b) 24c) 18d) 12Correct answer is option 'C'. Can you explain this answer? covers all topics & solutions for SSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for At their usual efficiency levels, A and B together finish a task in 12 days. If A had worked half as efficiently as she usually does, and B had worked thrice as efficiently as he usually does, the task would have been completed in 9 days. How many days would A take to finish the task if she works alone at her usual efficiency?a) 36b) 24c) 18d) 12Correct answer is option 'C'. Can you explain this answer?.
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