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

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

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New post 13 Oct 2013, 22:54
i guess the fastest approach for such problems is to substitute values.

Given that x=4y; when y=1 then
Time taken by A = 4 hrs (x) -- A's rate = 1/4
Time taken by B = 1 hrs (y)--- B's rate =1

The question asks the % decrease in x ; So we need to find the time taken by A in order to complete the work in 3y/8 or 3/8 hrs. Basically the question is asking to find the percentage decrease in A's original time of 4 hrs...

eqn : 1/A + 1 = 8/3 or A=3/5 hrs

% Change =( 4-(3/5) )/4 =17/20 = 85%

I believe with this approach the problem can be solved in under 90 sec
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Re: Machine A currently takes x hours to complete a certain job.  [#permalink]

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New post 13 Oct 2013, 23:05
I guess the quickest number to solve such problems is to pick numbers
Given x=4y (Put y=1)

Time taken by A = 4 hrs or A's rate = 1/4
Time taken by B= 1 hr or B's rate = 1

Asked for the % reduction in A's time (4hrs) to complete the work in 3/8 hrs.
1/A+1=8/3 or A=3/5 hrs

% Change = (4-(3/5)) / 4 = 17/20 = 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 Feb 2014, 00:27
This problem can also be solved in one equation.

\(\frac{1}{4y*((100-d)/100)} + \frac{1}{y} = \frac{8}{3y}\)

Where d represents the percentage decrease. Rearrange the formula and cancel out y.

\(\frac{25}{100-d}=\frac{8}{3}-\frac{3}{3}\)

\(\frac{25}{100-d}=\frac{5}{3}\)

\(75=500-5d\)

\(5d=425\)

\(d=85\)
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Re: Machine A currently takes x hours to complete a certain job.  [#permalink]

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New post 06 Apr 2015, 03:14
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%



Let y be 8
=> x = 32

let total units of work to be done is 32 units

so a does 1 unit/hr
and b does 4 unit/hr

now we are asked to complete the work in 3y/8 or 3*8/8 = 3 hrs

so we would need to complete 32/3 = 10.66 units/hr
right now we are doing 5 units, so a would actually need to do 6.66 units/hr

so a would complete all the work in 32/6.66 = 4.80 hrs

hence x is reduced by (32-4.8)/32 = 0.85 or 85%
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Re: Machine A currently takes x hours to complete a certain job.  [#permalink]

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New post 06 Apr 2015, 03:47
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%


My solution :
Let rate for Machine A after decrease = x-a, where a is %. Therefore, per hour rate for Machine A is 1/x-a
For machine B 1/y
Combined rate after the above adjustment
1/(x-a)+1/y and work completed in one hour is 8/3y
Solving 1/(x-a)+1/y=8/3y will give a=17/20 which if converted into % would be 85%. Hence, the answer is E
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Re: Machine A currently takes x hours to complete a certain job.  [#permalink]

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New post 18 Mar 2016, 19:27
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%


time a+b = 3y
jobs done by a+b in 3y = 8
rate a+b = 8/3y
new rate a = 8/3y - 1/y = 5/3y
time to finish 1 job for new rate of A is 3y/5
initial time of A = 4y.
by what coefficient do we need to multiply 4y to get 3y/5? => by 3/20
3/20 = 15/100, which is the coefficient for 85% decrease

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

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New post Updated on: 21 Dec 2017, 05:59
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%

If A takes x hours and B takes y hours then A and B together can complete the same work in x*y/x+y hours.
By supposition, x*y/x+y = 3*y/8
8*x*y=3*x+3*y
x=3*y/5
It is given x=4*y
Therefore, ((4*y-3*y/5)/4*y)*100
85%

Originally posted by Mathivanan Palraj on 18 Mar 2016, 21:06.
Last edited by Mathivanan Palraj on 21 Dec 2017, 05:59, 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 04 Apr 2016, 01:56
Use formula xy/x+y=total time
Time given is 3y/8=xy/x+y.
Also given is x=4y
Let Y =1
Put value of y in the above formula.
x/x+1=3/8 solving =x=5/3
But we are given x=4 and above value is the reduced time.
Hence
4-5/3/4*100=1700/20=85%

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

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New post 04 Apr 2016, 14:21
x=A's time to complete job
y=B's time to complete job
old x/y relationship:
x=4y hours
new x/y relationship:
combined A+B time for job=3y/8 hours
1/x+1/y=1/(3y/8) combined A+B rate
x=3y/5 hours
ratio of new/old x times:
(3y/5)/4y=3/20=15%
100%-15%=85% decrease in x
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Re: Machine A currently takes x hours to complete a certain job.  [#permalink]

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New post 28 Jan 2020, 00:16
A's time X h. = 4Y h.
B's time Y h.
We want them both to work for 3Y/8 hours, and it's reciprocal gives us their combined rate:
8/3Y = 1/X + 1/Y => 1/X = 8/3Y - 1/Y = 5/3Y; X= 3Y/5;

and the percent of decrease from 4Hours to 3Y/5 with this formula "change/original *100" is:
((4Y - 3Y/5)/ 4Y) * 100 = 17Y/5 * 1/4Y *100 = 85%.
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Machine A currently takes x hours to complete a certain job.  [#permalink]

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New post 28 Jan 2020, 02:10
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 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
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Machine A currently takes x hours to complete a certain job.   [#permalink] 28 Jan 2020, 02:10

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