Machine A can complete a job in 12 hours and has worked for 4 hours on

Question

Machine A can complete a job in 12 hours and has worked for 4 hours on it. Machine B operates at a rate that is 2/3 of machine A's rate. How many more hours does machine B need to work alone to finish the remaining part of the job?

A. 12 hrs
B. 16 hrs
C. 24 hrs
D. 28 hrs
E. 32 hrs

A. 12 hrs 
B. 16 hrs 
C. 24 hrs 
D. 28 hrs 
E. 32 hrs

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Machine A can do a job in 12 hours at a constant rate and machine A do the job in 4 hours. Machine B can do the same job at a 2/3 constant rate of machine A. If machine B does the rest job, what is the amount of hours done by machine B alone?

ruis · Answer

Using the percent approach presented on the Tips and Hints post (https://gmatclub.com/forum/tips-and-hin ... 72096.html) we assume that the task is 100%
A does 100% of the job in 12 hours (100work/12hours). After 4 hours, machine A would have completed aprox 33% of the job (12x = 100*4; x= 33% work)
B does 100% of the job at a rate that is 2/3 of machine´s A rate. This means, machine B es SLOWER than machine A.
Use the reciprocal to understand machine B work rate -- 3/2 of 12 = 18 hours. Hence, machine B does 100% of the job in 18 hours (100work/18hrs).
How many minutes does machine B take to complete the remaining aprox 67% of the job? (100%-33% that has already been completed by machine A)?
100x = 67*18; x = 1206/100; x= 12 hours (rounding)

Solution: 12 hours

Hope it helps!

Arya_S · Answer

Rate of A= 1/12
Rate of B= 2/3 * 1/12 =1/18
Therefore,
(Ra)*Time + (Rb)*time(b)=1

(1/12)*4 + (1/18)* time(b)=1
(1/18)*time(b)= 2/3
Therefore time(b)= Time taken by B to complete remaining work alone= (2/3)*18 = 12 Hrs

Abhishek009 · Answer

Let, the total work be 36 Units (LCM of 12 & 3)

Thus, efficiency of A is 3 ; Efficiency of B is 2

Work done by A in 4 Hours is 12 Units, work left is 24 Units...

Time required by B to complete the work is 24/2 = 12 Hours, Answer must be (A) 12 hrs

Archit3110 · Answer

rate of A = 1/12
work done in 4 hours ; 1/3
work left 2/3
rate of B = 1/12 * 2/3 ; 1/18
time it will take to complete 2/3 work
1/18 * x = 2/3
x = 12 hours
option A

Shubhradeep · Answer

Option A should be correct 
Easy one.

We know Time taken to complete a work ∝ 1/Efficiency

Machine A takes 12 hours to complete a work. So Machine B will take 12*1/(2/3) = 18 hours

If Machine A has worked for 4 hours, it has completed 1/3rd of the total work. It would have taken 8 more hours to complete the job.

So Machine B will take 8*3/2=12 hours

Hence, Option A should be correct.

Machine A can complete a job in 12 hours and has worked for 4 hours on

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Machine A can complete a job in 12 hours and has worked for 4 hours on

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