Machine A currently takes x hours to complete a certain job.

Question

Machine A currently takes x hours to complete a certain job. Machine B currently takes y hours to complete the same job. If x = 4y, and x decreases by 85 % what is the time taken by A and B together to complete the job in hours?

(A) 3y/8

(B) 2y/6

(C) y

(D) 6y/19

(E) 8y/3

Show Answer

Official Answer

A

(A) 3y/8

(B) 2y/6

(C) y

(D) 6y/19

(E) 8y/3

rajatchopra1994 · Answer

Dear  dracarys007 ,

You have modified this question which is already discussed here.  https://gmatclub.com/forum/machine-a-currently-takes-x-hours-to-complete-a-certain-job-142886.html

This is not original question from Manhattan also.

Regards,
Rajat Chopra

dracarys007 · Answer

Yes this is a modified question from Manhattan. I agree. But this question is interesting and can be solved both ways and is a good practice. If the moderator feels that this question should not be posted for practice please feel free to delete the question.

gurmukh · Answer

Initial efficiency of A is 1/4 th of efficiency of B.
Then new time taken by A becomes 3/20 of original time taken then new efficiency of A in terms of B
= 20/3×4 =5/3
So new combined efficiency of A and B i terms of B 
= 5/3 + 1=8/3
So time taken will be 3/8 of the original time taken so 3/8y

Posted from my mobile device

CrackverbalGMAT · Answer

Time and Work requires using the concept of converting time into work and vice versa
For e.g if I can do a piece of work in 10 hours, then every hour I can do 1/10th of the work. The reverse is that if I do 1/5th of the work in 1 hour, then I can finish the work in 5 hours.

We are given that time for m/c A = 4 times the time taken for m/c B

Therefore if B takes y units of time, A would take 4y units of Time

A's time is now decreased by 85%, i.e now it is (100 - 85) = 15% of its original time = (15/100) * 4y = 3y/5 units of time.

Amount of work done by m/c A in 1 unit of time = 1 / (3y/5) = 5/3y

Amount of work done by m/c B in 1 unit of time = 1 / y

Therefore the total work done bu both A and B in 1 unit of time = (5 / 3y) + (1/y) = (5 + 3) / 3y = 8/3y

Therefore the time taken when both work together (we flip the numerator and denominator) = 3y/8 units of Time

Option A

Arun Kumar

Kinshook · Answer

Given: Machine A currently takes x hours to complete a certain job. Machine B currently takes y hours to
complete the same job. 
Asked: If x = 4y, and x decreases by 85 % what is the time taken by A and B together
to complete the job in hours?

Work of A & B together for one day =  \frac{1}{4y*.15} + \frac{1}{y} = \frac{5}{3y} + \frac{1}{y} = \frac{8}{3y} 
Time taken by A and B together to complete the job in hours =  3y/8

IMO A

ScottTargetTestPrep · Answer

Solution:

We can let the original value of x = 100; thus, y = 25, and the new value of x is 15. Therefore, the job will take 1/(1/15 + 1/25) = 1/(5/75 + 3/75) = 1/(8/75) = 75/8 hours to complete when the two machines work together. Notice that y = 25, so 75/8 = 3y/8.

Alternate Solution:

After x is decreased by 85%, machine A can do the job in 15x/100 = 3x/20 hours. Thus, in one hour, machine A can do 20/3x of the job and machine B can do 1/y of the job. Working together, 20/3x + 1/y of the job is done in one hour. Substituting x = 4y, we get:

20/3(4y) + 1/y

5/3y + 1/y

5/3y + 3/3y

8/3y

Since 8/3y of the job is done in one hour, it will take 1/(8/3y) = 3y/8 hours to complete the job.
 
Answer: A

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Machine A currently takes x hours to complete a certain job.

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