A alone completes a job in x days, and B alone completes it in y days.

Question

A alone completes a job in x days, and B alone completes it in y days. When they work together, they finish 3/20 of the job per day. If A and B worked together for 5 days and A needed to work independently for the additional 3 days to complete the job, what is the value of x + y?

A. 20
B. 21
C. 25
D. 27
E. 29

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A. 20
B. 21
C. 25
D. 27
E. 29

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dhart · Answer

it may be 20 days , i thinkk

Renchinjav · Answer

(1/x+1/y)=3/20 
(1/x+1/5)*5+3/x=1 => (1/x+1/y)= (1-3/x)*1/5=3/20=>x=12
y= 3/20-1/12=1/15 
Hence, x+y=27

dhart · Answer

With calculation, it comes to

(1/x+1/y)*5+3/x=1
1/x+1/y= (1-3/x)*1/5=3/20;
x=12
y=15
x+y=27

icandoit4u · Answer

Person time rate work  
   A 
 x 
 1/x 
 1 
 
  B 
 y 
 1/y 
 1 
 
  A+B 
 20/3 
 3/20 
 1 
 
  A+B 
 5 
 3/20 
 15/20=3/4 
 
  A 
 3 
 1/12 
 1/4

in the fourth row we find the word done together and from that we can find the work that a had to do alone which is 1-3/4 = 1/4 
with this we get x as 12 and to find y we can add rate of x and y with their total rate that is 3/20 so 1/x+1/y = 3/20
1/12+1/y=20/3 which gives 1/y as 1/15 so y = 15
 x+y = 12+15= 27

Mohana21Lakshmi · Answer

(3/20)/1=t/5; t=3/4
together for five days A and B completed 3/4 of the work and remaining 1/4 of work completed by A in 3 days, therefore; 1/x=(1/4)/3; x=12days
working together 1/x+1/y=(3/4)/5; 1/12+1/y=3/4*1/5; 1/y=3/20-1/12; 1/y=4/60; y=15 days 
x+y = 15+12 days =27 days

counterclash1 · Answer

Correct Answer: D (27)

GIVEN:
- Combined Rate = 3/20 job/day
- Together time = 5 days
- A alone time for remaining = 3 days

STEP 1: WORK DONE TOGETHER
- Work = 5 * (3/20) = 15/20 = 3/4
- Remaining work = 1 - 3/4 = 1/4

STEP 2: FIND A'S RATE AND x
- A's rate = (1/4) / 3 = 1/12
- x = 12 days

STEP 3: FIND B'S RATE AND y
- B's rate = 3/20 - 1/12 = 9/60 - 5/60 = 4/60 = 1/15
- y = 15 days

STEP 4: SUM x + y
- x + y = 12 + 15 = 27

Conclusion: Answer Choice D.

SS990 · Answer

no. 
 w 
 r 
 t 
 
  a 
 1 
 1/x 
 x 
 
  b 
 1 
 1/y 
 y 
 
  a+b 
 3/20 
 1/x+1/y 
 1

1/x+1/y=3/20 
5/x+5/y=15/20=3/4

5/x+5/y+3/x=1
3/4+3/x=1   
solving for x
x=12
subtituting in one of equations above for y
y=15
x+y=27 (D)

madsb18 · Answer

Total Work = 60 units. Why 60 Units? 3/20 mentioned. Choose a convenient no.

A's rate of work 60/x. B's rate of work . 60/y.

together 60/x + 60/y = 3/20 * 60 = 9

They work together for 5 days. work completed 5*9 = 45 units. Work left 15 units (60-45)
A does 15 units of work in 3 days.
60/x * 3 = 15. x = 12.

y = 15.

x+y = 27.

A alone completes a job in x days, and B alone completes it in y days.

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GMAT Problem Solving (PS) Questions

A alone completes a job in x days, and B alone completes it in y days.

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