Time and Work
Aptitude

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Q.

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:

 A.

4 weeks

 B.

5 weeks

 C.

7 weeks

 D.

None of these

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Solution:
Option(A) is correct

2 weeks work of Aditya, Vedus and Yuvraj

\(2\left[\dfrac{1}{6}+\dfrac{1}{9}+\dfrac{1}{12}\right]=\dfrac{26}{36}\)

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

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

⇒ $x$ weeks work of both

\(x\left[\dfrac{1}{9}+\dfrac{1}{12}\right]=\dfrac{7x}{36}\)

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)


Rupesh
 ()

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



Dan
 ()

Alternate solution:

Work completed in 2 weeks:

$2*(1/6+1/9+1/12)=x$

$x=0.72$

Amount of work left :

$1-0.72=0.28$

Aditiya left.

$x$ is the remaining time:

$x/12+(x-1)/9=0.28$

$x=2$

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.


Deepak
 ()

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


Shubham
 ()

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?


Deepak
 ()

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