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

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Machine A currently takes x hours to complete a certain job.  [#permalink]

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New post 22 Nov 2012, 13:24
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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 3y/8 hours ?

A. 15%
B. 25%
C. 30%
D. 62,5%
E. 85%
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Re: Machine A currently takes x hours to complete a certain job.  [#permalink]

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New post 23 Nov 2012, 02:22
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superpus07 wrote:
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 3y/8 hours ?

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


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.
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Re: Machine A currently takes x hours to complete a certain job.  [#permalink]

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New post 22 Nov 2012, 21:36
1
According to the question:

Mac. A----x hrs-----1 job
Mac B----y hrs----1 job

also x=4y

let a be the factor by which x gets reduced so that both Mac. A and B complete the job in 3y/8 hrs

so new x=x'=4ay

then according to the question

[1/(4ay)]+[1/y]=[8/(3y)]

on solving we get

a=3/20

therefore x'=3/(5y)

now for the percentage decrease (pd)

pd= [(x-x')/x]*100
= [{4y-(3/5y)}/4y]*100
= 17/20*100
= 85%

hence the OA is


Please suggest any faster approach
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Re: Machine A currently takes x hours to complete a certain job.  [#permalink]

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New post Updated on: 22 Nov 2012, 23:45
1
superpus07 wrote:
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.

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-[15y/40]/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.
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Originally posted by Marcab on 22 Nov 2012, 23:11.
Last edited by Marcab on 22 Nov 2012, 23:45, edited 1 time in total.
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Re: Machine A currently takes x hours to complete a certain job.  [#permalink]

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New post 22 Nov 2012, 23:24
1
Marcab wrote:
superpus07 wrote:
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.

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.
\(reduction in time=\frac{4y}{5} - \frac{3y}{8}= \frac{15y}{40}\)

Only A is credited with this reduction of time.
Percentage decrease=4y-[15y/40]/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.



The percentage decrease exactly comes to be 17/20. which is 0.85 or 85%, i think there is some mistake in your calculations...there is no approximate value
its only the percentage decrease in X we have to calculate, not their combined time, so you approach is not totally correct.
..however you got the correct answer
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Re: Machine A currently takes x hours to complete a certain job.  [#permalink]

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New post 22 Nov 2012, 23:49
jkaustubh wrote:
Marcab wrote:
superpus07 wrote:
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.

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.
\(reduction in time=\frac{4y}{5} - \frac{3y}{8}= \frac{15y}{40}\)

Only A is credited with this reduction of time.
Percentage decrease=4y-[15y/40]/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.



The percentage decrease exactly comes to be 17/20. which is 0.85 or 85%, i think there is some mistake in your calculations...there is no approximate value
its only the percentage decrease in X we have to calculate, not their combined time, so you approach is not totally correct.
..however you got the correct answer

yes there was a typo. the reduction in time is 17y/40 not 15y/40.
Moreover, I DID calculate the percentage decrease in X, with the help of the combined time. If you have found some mistake in my approach, you can let me know, otheriwse for faster calculations I feel this approach is better.
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Re: Machine A currently takes x hours to complete a certain job.  [#permalink]

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New post Updated on: 23 Nov 2012, 00:04
Marcab wrote:
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-[15y/40]/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.



in this step, Image

I'm not understanding why you're able to subtract a unit of time from the rate... the expression on the left is the addition of machine rate A and machine rate B, and the 2nd part is the expression of time required for machine A and B to complete the job together..... confused

I'm not understanding your solution much at all actually... agh

Originally posted by anon1 on 23 Nov 2012, 00:02.
Last edited by anon1 on 23 Nov 2012, 00:04, edited 1 time in total.
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Re: Machine A currently takes x hours to complete a certain job.  [#permalink]

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New post 23 Nov 2012, 00:03
3
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-(3y/5)]/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
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Re: Machine A currently takes x hours to complete a certain job.  [#permalink]

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New post 23 Nov 2012, 00:05
combined rate of work will be 5/4y and not 5y/4. This was the mistake hence the approximate values.

I am solving for the value that has been asked in the question? just plain simple solution, no fancy combine time stuff here!!

hope below explanation helps you

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-(3y/5)]/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

moreover you are not calculating the decrease in the time taken by machine A, why do you need to find the combined decrease, when it is not even asked in the question?
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Re: Machine A currently takes x hours to complete a certain job.  [#permalink]

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New post 23 Nov 2012, 00:14
Quote:
in this step, Image

I'm not understanding why you're able to subtract a unit of time from the rate... the expression on the left is the addition of machine rate A and machine rate B, and the 2nd part is the expression of time required for machine A and B to complete the job together..... confused

I'm not understanding your solution much at all actually... agh


Let me explain:
\(Rate of A=\frac{1}{x}\)
\(rate of B=\frac{1}{y}\)
\(Combined rate=(x+y)/xy\)
Since x=4y,
therefore combined rate=5y/(4y*y)=\(5/4y\)
Now \(Rate * time= Work\)
work=1, therefore time=\(\frac{1}{Rate}\).
Hence combined time=4y/5.
Hope that helps
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Re: Machine A currently takes x hours to complete a certain job.  [#permalink]

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New post 23 Nov 2012, 00:19
jkaustubh wrote:
moreover you are not calculating the decrease in the time taken by machine A, why do you need to find the combined decrease, when it is not even asked in the question?


I calculated the combined decrease because, because B continued to work at the same rate whereas A increased his speed and this increase only led to the combined time decrease.
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Re: Machine A currently takes x hours to complete a certain job.  [#permalink]

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New post 23 Nov 2012, 00:55
1
Given :

Time taken by machine A to complete a job = x hrs = 4y hrs

Time taken by machine B to complete the same job = y hrs

To find:

the percentage decrease in the time taken by machine A to complete the same job with machine B in 3y/8 hrs

Solution:

Let the new time taken by machine A to complete the job along with Machine B be x' so that they both do the job together in 3y/8 hrs.

So according to the question, we get the following equation

1/x'+1/y=8/3y

this gives us 1/x'=8/3y-1/y

on solving this we get x'=3y/5 hrs


now to calculate the percentage decrease in the time taken by machine A from case 1 (when machine A took x hrs to complete the job) to case 2 (when machine A took x' hrs to complete the job), we will use the old simple percentage formula i.e
%age decrease = [old value-new value]/old value*100
= [x-x']/x*100
= [4y-(3y/5)]/4y*100
= 17/20*100
= 85%

hope you get this detailed solution, only similar quantities are used in all the equations. Also you need not find the combine rate, as it is not asked in the question

Bhai, I cannot understand, what is so difficult in the approach that you are not able to understand, or it that you are so stubborn that its either your solution or no solution.
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Re: Machine A currently takes x hours to complete a certain job.  [#permalink]

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New post 23 Nov 2012, 03:29
Bunuel, can you please let me know where am I making the mistake. I took a different approach, intuitive rather, but I am not getting the exact answer.
Thanks in advance
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Re: Machine A currently takes x hours to complete a certain job.  [#permalink]

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New post 28 Sep 2013, 02:02
1
Good one !!

Rate (1) = 1/x
Rate(2) = 1/y

Combined rate = 1/x + 1/y = (x+y)/xy

Rate * Time = Work

Time = xy/(x+y) = 3y/8

x = 3/5y

Initially we are given that x=4y

% decrease = (Initial - Final)/Initial * 100
= (4y- 3/5y)/4y * 100

Hence (E)!
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Re: Machine A currently takes x hours to complete a certain job.  [#permalink]

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New post 10 Oct 2013, 07:20
Bunuel how do u get to be so smart, no matter how many questions I practice I still can't figure out the way in tough questions. :(
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Re: Machine A currently takes x hours to complete a certain job.  [#permalink]

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New post 10 Oct 2013, 19:07
Bunuel wrote:
superpus07 wrote:
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 3y/8 hours ?

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


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.



could you explain how you flipped the fraction over in there, I don't get any of what was done for this problem
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Re: Machine A currently takes x hours to complete a certain job.  [#permalink]

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New post 10 Oct 2013, 19:08
TGC wrote:
Good one !!

Rate (1) = 1/x
Rate(2) = 1/y

Combined rate = 1/x + 1/y = (x+y)/xy

Rate * Time = Work

Time = xy/(x+y) = 3y/8

x = 3/5y

Initially we are given that x=4y

% decrease = (Initial - Final)/Initial * 100
= (4y- 3/5y)/4y * 100

Hence (E)!


Where on Earth did you get that from? I can't wrap my head around it.
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Re: Machine A currently takes x hours to complete a certain job.  [#permalink]

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New post 10 Oct 2013, 22:23
AccipiterQ wrote:
TGC wrote:
Good one !!

Rate (1) = 1/x
Rate(2) = 1/y

Combined rate = 1/x + 1/y = (x+y)/xy

Rate * Time = Work

Time = xy/(x+y) = 3y/8

x = 3/5y

Initially we are given that x=4y

% decrease = (Initial - Final)/Initial * 100
= (4y- 3/5y)/4y * 100

Hence (E)!


Where on Earth did you get that from? I can't wrap my head around it.



Hi there,

Can you be more specific about which part of the solution you didn't get?

I am happy to explain that !

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Re: Machine A currently takes x hours to complete a certain job.  [#permalink]

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New post 11 Oct 2013, 01:44
1
3
superpus07 wrote:
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 3y/8 hours ?

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


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%
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Re: Machine A currently takes x hours to complete a certain job.  [#permalink]

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New post 11 Oct 2013, 02:03
1
AccipiterQ wrote:
Bunuel wrote:
superpus07 wrote:
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 3y/8 hours ?

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


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.



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


\(\frac{1}{(\frac{3y}{8})}=1*\frac{8}{3y}=\frac{8}{3y}\).
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Re: Machine A currently takes x hours to complete a certain job. &nbs [#permalink] 11 Oct 2013, 02:03

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