D01-30

Question

Painter A can paint a house alone in 20 days, while Painter B can do it in 30 days. They began painting a house together, but at some point, A left for a number of days before rejoining B to finish the job. B worked alone for 5 days, and then A and B together completed the remaining work in 4 days. How many days did A and B work together before A initially left B?

A. 4
B. 5
C. 6
D. 7
E. 8

Show Answer

Official Answer

C

A. 4
B. 5
C. 6
D. 7
E. 8

Bunuel · Accepted Answer

Official Solution:

Painter A can paint a house alone in 20 days, while Painter B can do it in 30 days. They began painting a house together, but at some point, A left for a number of days before rejoining B to finish the job. B worked alone for 5 days, and then A and B together completed the remaining work in 4 days. How many days did A and B work together before A initially left B?

A. 4
B. 5
C. 6
D. 7
E. 8

Show Answer

Official Answer

C

A. 4
B. 5
C. 6
D. 7
E. 8

Painter A has a rate of  \frac{1}{20}  job/day, while Painter B has a rate of  \frac{1}{30}  job/day.
 
The combined rate of A and B working together is  \frac{1}{20}+\frac{1}{30}=\frac{1}{12}  job/day.
 
During the 5 days that B worked alone (second stage), B completed  5*\frac{1}{30}=\frac{2}{12}  of the job.
 
In the 4 days that A and B worked together (third stage), they completed  4*\frac{1}{12}=\frac{4}{12}  of the job.
 
Therefore, during the first stage of work, A and B together completed  1-(\frac{2}{12}+\frac{4}{12})=\frac{6}{12}  of the job. At their combined rate of  \frac{1}{12}  job/day, it took them 6 days to complete this portion of the job.

Answer: C

Mo2men · Answer

Given from the prompt:

A & B worked together + B worked alone + A& B joined again to complete work

Combined rate = 1/20+ 1/30 = (3+2)/60=5/60= 1/12 job/day

Let T= time for both A & B together before A leaving B

To solve the question:

Use the standard formula

Work = rate * time

Following the sequence stated by prompt

T *1/12 + 5 *1/30 + 4 *1/12 = 1 .............( the work here is one house)

T /12 + 1/6 + 1/3 = 1

T /12 + 3/6= 1

T /12 = 1/2 .......T=6

Answer: C

swanidhi · Answer

I prefer assuming total work before solving such questions. Helps me to avoid fractions.

ALONE
A finishes work in 20 days
B finishes work in 30 days

Taking LCM of 20 and 30 (Or any convenient common mulitple) --> 120
So if total work is 120, then to finish 120 units of work as per their current rate
A finishes work 120/20 = 6 units per day
B finishes work 120/30 = 4 units per day
Both together finish 6 + 4 = 10 units per day.

Coming back to what's asked -
B alone worked for 5 days, so 4*5 = 20 units of total 120 units is done
Together they worked for 4 hours before finishing the work = 10*4 = 40 units.
We've got 40 + 20 = 60 units done.
120-60 = 60 units pending.
This work is nothing but the work that A & B did together before A left B alone to suffer.
Hence 60/10 = 6 days!

gbernad · Answer

I think this is a  high-quality  question and I agree with explanation.

PerseveranceWins · Answer

I think this is a  high-quality  question and I agree with explanation.

tae808 · Answer

I think this is a  high-quality  question and I agree with explanation. Great question. I freaked out when I first faced it but was able to solve it within 2 mins! Thanks

IAmKrish · Answer

I will go with this approach,

rate of A= 1/20 job per day
rate of B = 1/30 job per day

when they work together the no of days required to complete the task = 1/20 + 1/30 = 3+2/60 = 5/60 = 1/12

when A and B were working together let us assume that after X days A left the working while , 
so the work completed in X days by both of them = x * 1/12= x/12

so the work remaining = 1-x/12 = 12-x/12

Now B worked for 5 days , so total work done by B in 5 days = 5*1/30 = 1/6

now the total work remaining = total work remaining after x days - work done alone by B in 5 days 
 = 12-x/12 - 1/6
 = 10-x/12

now A rejoined the work and they both completed the remaining work in 4 days 
remaining work = 4 days of work for A and B 
10-x/12 = 4/12
10-x = 4
x= 6

so the no of days after which A left working together is 6

praveen27sinha · Answer

let for x days A worked with B before he left 
Now
A worked for X+ 4 days
B worked for X+4+5 ie. X+9 days.

(X+4)/20 + (x+9)/30 =1
solve this you will get X=6

SabuzBD · Answer

I think this is a  high-quality  question.

swats1903 · Answer

I think this is a  high-quality  question and I agree with explanation.

SushiVoyage · Answer

Let's pick up a Number which is the LCM of both of A and B's rates, for eg. 60.
Here, let 60 be the total units of work to be done.

So, if A takes 20 days to finish 60 units, it means he accomplishes 60/20= 3 units per day.
Similarly, if B takes 30 days to finish 60 units, he accomplishes 60/30= 2 units per day

Now, the total work done by them in 1 day= 3+2= 5 units.

For the 5 days B worked by himself, he gets 5*2 units= 10 units done.
The 4 days A and B work together in the end, they get 4* 5 units= 20 units done.
Total work done= 30 units.
Leftover work= 60-30 units= 30 units. This is the work that A and B must have done together, before A left.

So, given the combined rate, A and B together must have done 30 units in 30/5= 6 days!

Bunuel · Answer

I have edited the question and the solution by adding more details to enhance its clarity. I hope it is now easier to understand.

aviral12567 · Answer

I think this is a  high-quality  question and I agree with explanation. I agree with the explanation just I want to point out that the work done in second stage, can you explain why you considered 5*1/30= 2/12

Bunuel · Answer

In the second stage, B worked alone for 5 days at the rate of  \frac{1}{30}  job/day, hence completed  5*\frac{1}{30}=\frac{2}{12}  of the job.

BottomJee · Answer

I think this is a  high-quality  question and I agree with explanation.

sb995 · Answer

I did not quite understand the solution. Could you please suggest a way to estimate the answer to this problem without using algebra? Thank you.

Bunuel · Answer

The options are quite close to each other, so this may not be a good candidate for estimation. However, the algebra and approach used in the solution are very straightforward. If you take the time to understand it, the question becomes much easier. If it’s still not clear, please ask specific questions about what part is confusing so I know what to elaborate on. Alternatively, you can check other solutions in the thread above.

kmotwani · Answer

I like the solution - it’s helpful.

agrasan · Answer

I like the solution - it’s helpful.

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