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, by what percent will x have to decrease so that A and B together can complete the job in \(\frac{3y}{8}\) hours ?

A. 15%
B. 25%
C. 30%
D. 62,5%
E. 85%

Thanks.

A. 15%
B. 25%
C. 30%
D. 62,5%
E. 85%

Bunuel · Accepted Answer

We need  x  to decrease so that A and B together can complete the job in  \frac{3y}{8}  hours, so we need the combined rate of machines A and B to be  rate=\frac{job}{time}=\frac{1}{(\frac{3y}{8})}=\frac{8}{3y}  job/hour -->  \frac{1}{x}+\frac{1}{y}=\frac{8}{3y}  -->  x=\frac{3y}{5}  hours.

We have that in order A and B together to complete the job in  \frac{3y}{8}  hours, the time in which machine A completes the job must be  \frac{3y}{5}  hours instead of  4y  hours.

Percentage decrease should be  \frac{change}{original}*100=\frac{4y-\frac{3y}{5}}{4y}=85% .

Answer: E.

Hope it's clear.

KarishmaB · Answer

You can also do this question by assuming values.

A takes x hrs, B takes y hrs. 
x = 4y
Together they need to take 3y/8 hrs so x needs to be reduced.
Say y = 8.

A takes x = 4*8 = 32 hrs alone
B takes 8 hrs alone.
Together they need to take 3*8/8 = 3 hrs.

They need to complete (1/3) work every hr. Machine B does (1/8)th of the work every hr. So machine A needs to do 1/3 - 1/8 = 5/24 of the work every hr.
i.e to complete the work, machine A should take only 24/5 hrs alone. Currently it takes 32 hrs.
Required reduction = (32 - 24/5)/32 *100 = 85%

Marcab · Answer

The question intends to say that A has increased his rate of work and as a result, the total time taken by both of them has also decreased.
Consider the initial time that was supposed to be taken by both of them.
 \frac{1}{x} + \frac{1}{y}  is the combined rate of work.
Since  x=4y ,
hence combined rate of work will come out to be  \frac{5y}{4} .
Since the work is 1 unit, therefore time required at this rate to complete this much of work will be  \frac{4y}{5} .
BUT, they are supposed to complete the work in  \frac{3y}{8}  hours. So first we calculate the reduction in total time.
 reduction in time=\frac{4y}{5} - \frac{3y}{8}= \frac{17y}{40}

Only A is credited with this reduction of time.
Percentage decrease=4y- /4y
=(29/32)*100.
We need not calculate thsi value because if we see the options, only E is close to this value.
Hence E.

jkaustubh · Answer

Let Machine A take x' hours to complete the job so that both machines A and B can complete the job in 3y/8 hrs.
now 
1/x'=8/3y-1/y

this gives x'=3y/5
now calculate the %age decrease

i.e
 /4y=17/20=0.85

this was my approach. not sure abt your calculation speed, but it took me less that a min to solve it

AccipiterQ · Answer

could you explain how you flipped the fraction over in there, I don't get any of what was done for this problem

Bunuel · Answer

\frac{1}{(\frac{3y}{8})}=1*\frac{8}{3y}=\frac{8}{3y} .

sujoykrdatta · Answer

We can assume a suitable value of y (and hence x) and calculate the answer: 
Let y = 8 hours => Time taken by B to complete the work = 8 hours
=> x = 32 hours => Time taken by A to complete the work = 32 hours

Note: At the above rates, fraction of work done by A and B in 1 hour = 1/8 + 1/32 = 5/32 
 => Time taken by A and B together to complete the work = 32/5 hours

However, we need to complete the work in 3y/8 = 3 hours

Thus, in each hour, A and B should do 1/3 rd of the work 
=> Work done by A in 1 hour (after the value of x is changed) = 1/3 - 1/8 = 5/24

=> Time (new) taken by A to complete the work = 24/5 = 4.8 hours

The question asks: "what percent will x have to decrease"
Thus, it is asking about the percent change in time

=> Required percent = (32 - 4.8)/32 * 100 = 85%

Answer E

GMATGuruNY · Answer

Let y=8 hours and x=32 hours, implying that the desired time for the job  = \frac{3y}{8} = \frac{3*8}{8} = 3  hours.

Let the job = LCM(8, 32, 3) = 96 units.
Since A takes x=32 hours to produce 96 units, A's rate  = \frac{work}{time} = \frac{96}{32} = 3  units per hour.
Since B takes y=8 hours to produce 96 units, B's rate  = \frac{work}{time} = \frac{96}{8} = 12  units per hour.

Required rate to complete the 96-unit job in the desired time of 3 hours  = \frac{work}{time} = \frac{96}{3} = 32  units per hour.
Since B's rate = 12 units per hour, A's rate must increase from 3 units per hour to 20 units per hour.
Rate and time have a RECIPROCAL RELATIONSHIP.
Since A's new rate is 20/3 of its current rate, A's new time must be 3/20 of its current time, a decrease of  \frac{17}{20} =  85%.

E

Manifesting710 · Answer

I took a longer approach, might be helpful to someone
 
Rate A = \frac{1}{X}
Rate B = \frac{1}{Y}
 X = 4Y

\frac{1}{X} + \frac{1}{Y} = \frac{8}{3Y}

\frac{1}{4Y} + \frac{1}{Y} = \frac{8}{3Y}
 
  \frac{1}{4Y*(P/100)} + \frac{1}{Y} = \frac{8}{3Y} , Where  P = 100 - x,  x is what we need to find 
 
\frac{1}{4Y*(P/100) } + \frac{1*4*(P\100) }{Y*4*(P/100) } = \frac{8}{3Y}
 
simplifying
 \frac{ 1 + (P\25)}{ (PY/25)  } = \frac{8}{3Y}

Simplifying
 
3Y = \frac{8PY}{25} - \frac{3PY}{25}

3Y = \frac{5PY}{25}
 
P = 15

P = 100 - X -> X = 85 , Hence (E)

Him2323 · Answer

Hello, I checked the value of the calculation in the last part. It's coming out to be 90.6%. Can you please re-check the method employed?

bumpbot · Answer

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

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