Aditya, Vedus and Yuvraj alone can do a job for 6 weeks, 9 weeks and

Question

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. 8 weeks

E. 9 weeks

A. 4 weeks
B. 5 weeks
C. 7 weeks
D. 8 weeks
E. 9 weeks

CrackverbalGMAT · Answer

Work done by Aditya in 1 week = 1/6

Work done by Vedus in 1 week = 1/9

Work done by Yuvraj in 1 week = 1/12

Work done by all together in 1 week =  \frac{1}{6} + \frac{1}{9} + \frac{1}{12} = \frac{6 + 4 + 3}{36} = \frac{13}{36}

Work done in 2 weeks =  2 * \frac{13}{36}= \frac{13}{18}

Work remaining =  1 - \frac{13}{18} = \frac{5}{18}

Since Yuvraj is the person finishing the work after Aditya Leaves, let us assume he work on the remaining part for x weeks.

Vedus leaves 1 week before completion, so he works on it for x - 1 weeks after Aditya leaves.

Fraction of work done by Yuvraj =  \frac{x}{12}

Fraction of work done by Vedus =  \frac{x - 1}{9}

The sum of these fractions is equal to the remaining work. So  \frac{x}{12} + \frac{x - 1}{9} = \frac{5}{18}

LCM = 36. Therefore 3x + 4(x - 1) = 10

3x + 4x - 4 = 10

7x = 14

x = 2

The job takes 2 + 2 = 4 weeks

Option A

Arun Kumar

acemeister29 · Answer

Another approach

Let us assume that the total work which needs to be done is 36 units. (LCM of 6, 9 and 12)

Rate at which Aditya does work is 6 units a week. Similarly rate of work of Vedus is 4 units a week and for Yuvraj is 3 units a week.

Now the three work together for 2 weeks. Total work done would be (6+4+3)*2 = 26 units

Remaining work is 10 units. Assuming this work is done in n weeks.

Work done by Vedus = 4(n-1) units (as he leaves one week prior to completion of work)

Work done by Yuvraj (as he works for the whole time) = 3n units

Hence 4(n-1) + 3n = 10

Solving we obtain n=2

Therefore the total time taken to complete the work is 2+2 = 4 weeks. (The two weeks when all 3 were working plus the additional 2 weeks when Aditya had left and the remaining work was done by Vedus and Yuvraj)

This approach can eliminate fractions in solving the problem which people often find cumbersome)

Thanks,
Abhinav

Posted from my mobile device

H1ccups · Answer

A rate = 1 job / 6 weeks
V rate = 1 job / 9 weeks
Y rate = 1 job / 12 weeks

LCM 6, 9, 12 = 36

Write this job as a single equation:
A-term: 2/6 jobs completed in 2 weeks (1/6 jobs per week * 2 weeks)
V-term: (T-1)/9 jobs completed in working time (1/9 jobs per week * (T-1) weeks)
Y-term: T/12 jobs completed in working time (1/12 jobs per week * T weeks)

Combine:
(2/6)+(T-1)/9+(T/12)=1 job

Plug in choice B (T=5): (2/6)+(5-1)/9+(5/12) = (12/36)+(16/36)+(15/36)>1, 5 weeks is too long, answer is A

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Aditya, Vedus and Yuvraj alone can do a job for 6 weeks, 9 weeks and

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Aditya, Vedus and Yuvraj alone can do a job for 6 weeks, 9 weeks and

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