A can do a piece of work X in 5 days and works X and Y together in 11

Question

A can do a piece of work X in 5 days and works X and Y together in 11 days. If B takes 4 days to complete work Y, find the time taken by both A and B together to finish works X and Y.

A. 4 days
B. 4.4 days
C. 4.8 days
D. 5 days
E. 5.5 days

GMATbuster's Collection

GMATWhizTeam · Accepted Answer

Solution: 
 • Time taken by A to complete X = 5 days
• Time taken by A to complete X and Y = 11 days
 o Time taken by A to complete Y =  11 – 5 = 6  days 
• Time taken by B to complete Y = 4 days
• Let Y be the LCM of  (4, 6) 
 o Y =  LCM(4, 6) = 12  units
  Rate of A =  \frac{12}{6} = 2  units per day
 Rate of B =  \frac{12}{4} = 3  units per day
 Rate of A and B together =  2 + 3 = 5  units per day 
o A took 5 days to complete X
   X = Days* Rate = 5*2 = 10  units 
o Total work =  X + Y = 12 + 10 =22  units 
• Total time taken by A and B to complete X and Y =  \frac{22}{5} = 4.4  days 
Hence, the correct answer is  Option B.

chetan2u · Answer

A does Y in 11-5 or 6 days, while B does it in 4 days. 
Combined....1/6+1/4=10/24, that is 24/10 or 2.4 days

Now if A takes 6 days, A and B take 2.4 days ..
So if A takes 1 day, A and B will take 2.4/6 or 24/60
Finally if A takes 11 days, A and B will take 11*24/60=11*4/10=4.4 days

B

DhanyaAbhirami · Answer

GMATWhizTeam 
A person can have different working speeds for different tasks. 
The question doesn't provide how much time B takes to do work X alone or X and Y.
How can we use the combined work rate for work Y alone as use it for work X and Y?

Jxmes · Answer

find how long a does y then compare to how long b does y. then use ratio of rates for work y to infer b's rate for x from a's.

you're first statement is correct in the real world, but for this question you have assume that the ratio is uniform across tasks. there is no other way to solve it

PSKhore · Answer

A takes 5 days to complete work X, and (11-5) = 6 days to complete work Y.
B takes 4 days to complete work Y, but we don't know how many days it takes to complete work X.
However, we do know their rates of work. 
You can simply take a ratio of the time taken by both to complete work X, it will be the same for work Y.

For work X, their ratios will be 6:4 = 2:3
For work Y, 5:a = (2/3)*5

Now, you can simply find the time taken by A and B for each X and Y individually.
(1/6) + (1/4) = 2.4 days for X

(1/5) + (3/10) = (25/50) = 2 days for work Y

Now, add them  2.4 + 2 = 4.4 days

A can do a piece of work X in 5 days and works X and Y together in 11

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A can do a piece of work X in 5 days and works X and Y together in 11

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