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Aditya, Vedus and Yuvraj alone can do a job for 6 weeks, 9 weeks and 12 weeks respectively. They work together for 2 weeks. Then, Aditya leaves the job. Vedus leaves the job a week earlier to the completion of the work.

The job would be completed in:


4 weeks


5 weeks


7 weeks


None of these

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Option(A) is correct

2 weeks work of Aditya, Vedus and Yuvraj


Work left = \(1-\dfrac{26}{36}=\dfrac{10}{36}\)

Let Vedus works for $x$ weeks with Yuvraj after Aditya.

⇒ $x$ weeks work of both


The remaining work is done by Yuvraj in 1 week.

One week work of Yuvraj = \(\dfrac{1}{12}\)

\(\Rightarrow \dfrac{26}{36}+\dfrac{7x}{36}+\dfrac{1}{12}=1\)

$⇒ 29+7x=36$

$⇒ x=1$.

Vedus worked for 1 week with Yuvraj.

time to complete whole job,

2 weeks (all work together) + 1week (vedus and yuvraj works together) + 1 week alone yuvraj works

Hence total 4 weeks required.

Edit: Thank you shubham and Priyanka Dey for pointing out the correction in the comments. Now final answer is changed from 1 week to 4 weeks.

Edit 2: For an alternative solution, check comment by Dan.

(6) Comment(s)


let job would be completed in X days

solve equation

2[1/6+1/9+1/12] +X-3/9 + X-2/12 = 1

X= 4 week ans

2 week of work by three= 2[1/6+1/9+1/12]

remaining day=X-2

1 day earlier Vedus leaves the job. so vedus work X-3 week

so X-3 week work by vedus=X-3/9

and X-2 week work by yuvraj = X-2/12


Alternate solution:

Work completed in 2 weeks:



Amount of work left :


Aditiya left.

$x$ is the remaining time:



Total amount of time spent:

2 weeks (with all of them)+2 (including 1 week work of Vedus) = 4 weeks

Priyanka Dey

The question asks about the total time of completion i.e 4 week.


Thank you for letting us know the anomaly. Answer choice has been changed to reflect the correct answer now.


Here we require time to complete whole job,

2weeks(all work together)+1week(vedus and yuvraj works together)+1 week alone yuvraj works

hence total 4 weeks required..

now i have a doubt on que. format,

is it whle work or yuvraj with vedus?


Thank you for pointing out the aberration. Solution is updated to point to the correct answer choice now.