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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 c

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:

 

Option: 1

4 weeks


Option: 2

5 weeks


Option: 3

7 weeks


Option: 4

None


Answers (1)

Aditya's 1 week work = 1/6

Vedus's = 1/9

Yuvraj's = 1/12

Step 1 : work done for first 2 weeks 

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

LCM of 6,9,12 = 36

= 2 x (6+4+3)/36 = 2 x 13/36 = 26/36

Remaining work = 1 - 26/36 = 10/36

Step 2  : after 2 weeks aditya leaves .vedus and yuvraj work together 

Let total time = x weeks

So vedus , works ( x - 3 ) weeks ( he leaves 1 week before ends )

Yuvraj works full ( x - 2 ) weeks 

Work done after Aditya left :

= ( x - 3 ) x 1/9 + (x-2) x 1/12

= (4x - 10 )/36

This must equal to remaining work:

(4x - 10 )/36 = 10/36

4x - 10 = 10

4x = 20

x = 5

Answer : option 2 - 5 weeks

 

Posted by

Kavya S P

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