Machines A and B, working simultaneously at their respective constant

Question

Machines A and B, working simultaneously at their respective constant rates produce m units in 1 hour. If working independently it takes machine B 3 hours less than machine A to produce 2m units, how long does it take machine A to produce 5m units?

A. 1 hour
B. 2.4 hours
C. 2.5 hours
D. 6 hours
E. 15 hours

A. 1 hour
B. 2.4 hours
C. 2.5 hours
D. 6 hours
E. 15 hours

Bunuel · Accepted Answer

Machines A and B, working simultaneously at their respective constant rates produce m units in 1 hour. If working independently it takes machine B 3 hours less than machine A to produce 2m units, how long does it take machine A to produce 5m units?

A. 1 hour
B. 2.4 hours
C. 2.5 hours
D. 6 hours
E. 15 hours

A. 1 hour
B. 2.4 hours
C. 2.5 hours
D. 6 hours
E. 15 hours

On the PS section, always look at the answer choices before you start to solve a problem. They might often give you a clue on how to approach the question. 
 
If it takes machine B 3 hours less than machine A to produce  2m  units, then to produce  2m*2.5 = 5m  units, machine B will take  3*2.5 = 7.5  hours less than machine A. Thus, the time for A to produce  5m  units must be more than 7.5 hours. Only E fits.

Answer: E

peachfuzz · Answer

Rate of machine A is 2m/t
Rate of machine B is 2m / t-3

2m/t + 2m / t-3 = m
t here must equal 6 for this to be true

a quick ratio expression solves it
6/2m = x/5m
x= 15

Answer:E

Jackal · Answer

Hello all My attempt: Let the rate of Machine A be a units per hour and that of Machine B be b units per hour. From first statement we have a*1 + b*1 = m ........equation I From the second statement we have 2m/a - 2m/b = 3 ..........equation II We need to find out the value of \frac{m}{a} . Solving I and II and substituting x for \frac{m}{a} we get 2x^2 - 7x + 3 = 0 we get x = 0.5 or 3 and none of these exist in the options

so perhaps I am on the wrong path. Any help appreciated. My answers are 0.5 hours or 3 hours

Bunuel · Answer

The question is: how long does it take machine A to produce 5m units, not m units.

Jackal · Answer

Thanks.

Then the answer is  E   15 hours .

x=0.5 or 3 
But we need  5x  therefore  2.5 hours  or  15 hours . We reject the solution  x=0.5 hours  because it invalidates the statement 1.

chetan2u · Answer

hi,
i think the answer should be 3 for A and 1.5 for B...
Since A and B together produce m units together in 1 hr so individually it has to be more than 1..
secondly, the difference in producing 2m is 3 , so in producing m the difference will be 1.5...
this means ans for A> 1+1.5 ie 2.5... only D and E are there which dont fit in...
let A take x hr , B will take x-1.5 hr.....so 1/x + 1/(x-1.5)=1... 3 fits in... answer should be 3...

since answer is for 5m ans is 5*3=15

vishwaprakash · Answer

together A and B in 1 Hour can produce M units

A's 1 Hr + B's 1 Hr = M --- Equation 1

Let A takes x Hours to Produce 2M => A in one hour can produce 2M/X
As per the statement
B takes X-3 hours to produce 2M => B in one hour can produce 2M/(X-3)

Putting A's 1 hour and B's 1 Hour in equation 1

2M/X + 2M/(X-3) = M

on simplifying we will get
X = 1 or X = 6

X cannot be equal to 1, since as per the condition B takes (X-3) hours i.e -2 Hours to produce 2 M (Not possible)

Hence X = 6

A takes 6 Hours to Produce 2M
and hence 15 Hours to produce 5M

Option E

Bunuel · Answer

BTW the question has 1-minute shortcut solution. Without any equations.

Jackal · Answer

Would love to know some tricks! I am poor at these work type problems. I usually take the clean approach because I know this is not a strength area for me and thus my mind should not get muddled up after spending few seconds on the question.

Thanks!

Bunuel · Answer

Consider this: if together A and B produce 5m units in 5 hours (m in 1 hour). Can only A produce 5m in LESS than 5 hours? This eliminates A, B and C right away.

Now, can you tell me how can we eliminate the remaining incorrect answer?

viksingh15 · Answer

This is how I approached the question.

combined rate is m units in 1 hr and B takes 3 hrs less then A to produce 2m units.

Combined rate will take 2 hr to produce 2m units ( just to make same number of units) . Say A takes x hrs to produce 2m units, so B will take x-3 hrs to produce 2m units.

so we have equation

(combined rate) 1/2 = 1/x-3 + 1/x ( individual rates of A and B)

solving this we have => x^2 -7x +6 = 0, so we have two values of x = 1 & 6 ( 1 is not possible as this will make B's rate -ve)

so we have x=6, this is the rate of A.

Now A takes 6 hrs to produce 2m units and for 5m units he will take 15 hrs.

Soln E

King407 · Answer

6 hours is also not possible, if A takes 6 hrs to produce 5m => to produce 2m, A needs 12/5 hrs = 2.4 hrs.. Now B needs 3 hours lesser than A => 2.4 - 3 = negative value, which is not possible

To check E, if A takes 15 hrs to produce 5m => to produce 2m, A needs 6 hrs, and B needs 3 hours. (to cross check, A's rate = 1/3 and B's rate = 2/3 => m/hour rate)

Hence the answer is E

chetan2u · Answer

hi,

Since A and B together produce m units together in 1 hr so individually it has to be more than 1..
secondly, the difference in producing 2m is 3 , so in producing 5m the difference will be 7.5...
this means ans for A> 1+7.5 ie 8.5... only E LEFT...
ans 15 E

Kinshook · Answer

Given: Machines A and B, working simultaneously at their respective constant rates produce m units in 1 hour. 
Asked: If working independently it takes machine B 3 hours less than machine A to produce 2m units, how long does it take machine A to produce 5m units?

Let us assume machine A produces x units in 1 hour
Machine B produces (m-x) units in 1 hour

Time taken by machine A to produce 2m units = 2m/x hours
Time taken by machine B to produce 2m units = 2m/(m-x) hours

2m/x - 2m/(m-x) = 3
(2m(m-x) - 2mx)/x(m-x) =3
2m(m-2x) = 3x(m-x)
2m^2 - 4mx = 3mx - 3x^2
2m^2 - 7mx + 3x^2 = 0
2t^2 - 7t + 3 = 0 ; where t= m/x
2t^2 - 6t - t + 3 = 0
(2t-1)(t-3) = 0
t = 1/2 or t = 3

Definitely m>x ; t= m/x >1; t=3
t= m/x = 3
Take take by machine A to produce 5m units = 5m/x = 5t = 15 hours

IMO E

akadiyan · Answer

A and B working together takes 1 hour to produce M units --> This tells that working alone A would take more than 1 hour to complete M units.

So to produce 5M units, the time taken would definitely greater than 5 hours. We can eliminate options A,B and C.

Now in the remaining options, if we conider D, time taken to produce 5m units = 6 hours, then M units = 1.2 hours

So to produce 2m units, A would take 2.4 hours, but considering the information that B takes 3 hours less than A to produce 2m units, then B would take -0.4 hours to produce 2m units which is not possible.

So only possible option is E - 15 hours

Ans:   E

MuditKapoor · Answer

Rate at which A works is 1/A to produce 2m units in x hours. i.e. 1/A(x)= 2m 
to make 5 m units, the rate at which work is done can't obviously change. 
hence multiplying the equation by 2.5 both the sides gives us 
1/A(x)(2.5)= 5M

Framework is ready now;

Considering options A,B,C gives us a direct indication of -ve time hence can be rightly eliminated

for D&E

if 2.5x=6 
i.e. x=2.4 which again brings B's time to be -0.6 (Again an impossible scenario )

we are left with option E 
i.e.  2.5x=15 
x=6

therefore option E remains in the game.

BKD5050 · Answer

Hi. Thank you for the quick approach. Any similar questions to practice where we can apply such kind of shortcut?

Bunuel · Answer

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