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A
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Difficulty:
35%
(medium)
Question Stats:
72% (02:24) correct
28%
(02:36)
wrong
based on 122
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History
Date
Time
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Not Attempted Yet
X, Y and Z take 20, 30 and 60 days respectively to complete a job independently. They complete a job together. However Y leaves after 4 days and Z leaves after another 6 days. How many more days will it take for X alone to complete the job now?
A) 4
B) 3
C) 5
D) 6
E) 2
Posted from my mobile device
A) 4
B) 3
C) 5
D) 6
E) 2
Posted from my mobile device
25 Apr 2022, 00:07
Kudos
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Explanation:
When All worked together, they can complete work in 10days.
4 days they all worked together.
40% of work completed
When x & z work together they can complete all work in 15days.
So in another 6 days they will complete 40% of work.
Rest 20% work to be completed by x.
x completes whole work in 20days, so 20% of work will be completed in 4 days.
IMO-A
Hope it helps 12921
Posted from my mobile device
When All worked together, they can complete work in 10days.
4 days they all worked together.
40% of work completed
When x & z work together they can complete all work in 15days.
So in another 6 days they will complete 40% of work.
Rest 20% work to be completed by x.
x completes whole work in 20days, so 20% of work will be completed in 4 days.
IMO-A
Hope it helps 12921
Posted from my mobile device
25 Apr 2022, 01:57
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Hello 12921,
I don’t see a way in which Algebra is not used in solving the question. One way or the other, you will have to frame equations in solving this question and that would mean that you are using Algebra to solve this question.
However, by Algebraic method, if you meant the method of assuming work as 1 and obtaining the rates as fractions (THE method we all learned in school to solve questions on Rates) remember that it is not without its share of faults. Therefore, if you think logically, you can use smart values to set up equations and then use Algebra to solve them. Best of both worlds, give it a thought!
The equation to solve Time & Work questions is, Work = Rate * Time
The work can be assumed to be the LCM of 20, 30 and 60, which are the respective times taken by X, Y and Z when working independently.
Let work done = 60 units. To find out the respective rates, we use, Rate = \(\frac{Work }{ Time}\)
Rate of X = \(\frac{60 }{ 20}\) = 3 units per day
Rate of Y = \(\frac{60 }{ 30}\) = 2 units per day
Rate of Z = \(\frac{60 }{ 60}\) = 1 unit per day
At this stage, I have to mention that the question is poorly framed – “They complete a job together”, which is illogical. If that were the case, then we would not have a question at all. It probably means that they started working on the job together.
That sounds more logical.
Y leaves after 4 days. This means that all 3 of them worked together for 4 days.
Rate of X, Y and Z = 3 + 2 + 1 = 6 units per day.
Therefore, work done in 4 days = 24 units.
Remaining work = 36 units.
Z leaves after another 6 days. This means that X and Z work together for 6 days.
Rate of X and Z = 3 + 1 = 4 units per day.
Therefore, work done in 6 days = 24 units.
Remaining work = 36 – 24 = 12 units.
This work has to be completed by X alone. Working at 3 units per day,
Time taken by X to complete 12 units = \(\frac{12 }{ 3}\) = 4 days.
The correct answer is A.
I don’t see a way in which Algebra is not used in solving the question. One way or the other, you will have to frame equations in solving this question and that would mean that you are using Algebra to solve this question.
However, by Algebraic method, if you meant the method of assuming work as 1 and obtaining the rates as fractions (THE method we all learned in school to solve questions on Rates) remember that it is not without its share of faults. Therefore, if you think logically, you can use smart values to set up equations and then use Algebra to solve them. Best of both worlds, give it a thought!
The equation to solve Time & Work questions is, Work = Rate * Time
The work can be assumed to be the LCM of 20, 30 and 60, which are the respective times taken by X, Y and Z when working independently.
Let work done = 60 units. To find out the respective rates, we use, Rate = \(\frac{Work }{ Time}\)
Rate of X = \(\frac{60 }{ 20}\) = 3 units per day
Rate of Y = \(\frac{60 }{ 30}\) = 2 units per day
Rate of Z = \(\frac{60 }{ 60}\) = 1 unit per day
At this stage, I have to mention that the question is poorly framed – “They complete a job together”, which is illogical. If that were the case, then we would not have a question at all. It probably means that they started working on the job together.
That sounds more logical.
Y leaves after 4 days. This means that all 3 of them worked together for 4 days.
Rate of X, Y and Z = 3 + 2 + 1 = 6 units per day.
Therefore, work done in 4 days = 24 units.
Remaining work = 36 units.
Z leaves after another 6 days. This means that X and Z work together for 6 days.
Rate of X and Z = 3 + 1 = 4 units per day.
Therefore, work done in 6 days = 24 units.
Remaining work = 36 – 24 = 12 units.
This work has to be completed by X alone. Working at 3 units per day,
Time taken by X to complete 12 units = \(\frac{12 }{ 3}\) = 4 days.
The correct answer is A.
