Work Problem PS

Titleist · Joined: 03 Nov 2005 Posts: 1

I have a problems with this question (from Ascent Question Bank July, 5 2004):

A can complete a project in 20 days and B can complete the same project in 30 days. If A and B start working on the project together and A quits 10 days before the project is completed, in how many days will the project be completed?

(1) 18 days (2) 27 days
(3) 26.67 days (4) 16 days

Official Answer is 18 days

First off, it ambiguous if the question asks how many days will B ALONE take to finish the job or how many days TOTAL it will take to finish the job (the portion B alone worked plus the days A and B worked together).

Secondly, A and B have a combined rate of 1/12 and thus they will take 12 days alone to finish this job. If A quits 10 days before the project is completed, then there will be 10/12th or 5/6th of the job left for B alone to handle - thus 5/6 divided by 1/30 = 25 days for B to finish the rest of the job. If the question really is how many days B alone will take to complete the job after A quits, then the answer is 25.

If the question is how many days total the two workers will take to complete the job (including the portion that A worked TOGETHER with B plus the total number of days B worked alone after A quit) the answer should be 27 (A worked for only 2 days TOGETHER with B and B worked ALONE for 25).

Needless to say that I don't agree with the official explanation below for this question!

Explanatory Answer
If A can do complete a project in 20 days, then A will complete 1/20 th of the project in a day.
Similarly, B will complete 1/30th of the project in a day.
Let the total number of days taken to complete the project be x days.

(This is wrong because the combined rate of A and B must first be calculated since they did work together up until 10 days before the completion of the job. Their combined rate is 1/12 so it will take them both 12 days working together to complete this task. However A flakes out and quits on day 2. So B must complete 10/12 of the job at rate of 1/30 which is 25 days. So A and B worked together for 2 (using the combined rate of 1/12) and B worked alone for 25 days using B's independent rate of 1/30)

Then, B would have worked for all x days, while A would have worked for (x – 10) days.

(Since we know the combined rate of A and B, B worked with A for 2 days - this equation above is double counting the efforts of A and B together and their independent rates - which will lead understate the number of days spent completing the project)

Therefore, A would have completed X-10/20th of the project and B would have complete x/30 th of the project.
i.e., X-10/20 + X/30 = 1
Solving for x, we get x = 18.

Please tell me what I'm missing! Thank you.

satish · Joined: 20 Oct 2005 Posts: 2 Location: bangalore

hi

A&B together can complete the work in 12 days. now A quits from the work just 10 days before the work completed. this means that B worked 10 days after A quits. In the question it is given that if B alone work for 30 days he will complete the work. Now after A quits B worked for 10 days that is he completed alone 1/3 of the complete work. From this we come to know that they together completed 2/3 of the job that means they worked 8 days together(because it took 12 days to complete the work together). now the total no of days that took to complete the work is (8 days worked together + 10 days B alone worked ) 18 days.

i think this will make u clear ok all the best

Dumbo in CAT · Posted: Thu May 04, 2006 12:39 pm Post subject: Re: Work Problem PS

[quote="Titleist"]I have a problems with this question (from Ascent Secondly, A and B have a combined rate of 1/12 and thus they will take 12 days alone to finish this job. If A quits 10 days before the project is completed, then there will be 10/12th or 5/6th of the job left for B alone to handle - thus 5/6 divided by 1/30 = 25 days for B to finish the rest of the job. If the question really is how many days B alone will take to complete the job after A quits, then the answer is 25.

The mistake is in this para
You assumed B should do the "remaining 10/12th" of the work. The fact is that he should do the remaining 2/12th of the work. Not 10/12th which A & B have already completed together.

Heretic · Joined: 04 May 2006 Posts: 7 Location: Pune

First of all u need to decide when does A leave:

1. 10 days before the scheduled completion of the project.
2. 10 days before the actual completion of the project.

In this case it seems to me that A leaves 10 days before the "actual" completion, thus to solve u need to move backward.
As A moved out 10 days before the completion, B worked for those 10 days alone completing 33.33% work (B needs 30 days to complete 100%).
So remaining 66.66 (or 2/3) work must have been done by A and B together.
By unitary method u can say that
A+B --> 100% --> 12 days
A+B --> 66.66% --> 8 days

So finally A=B worked for 8 days together and then B finished the remaining work in 10 days.

So the answer is 18 (10+ Cool

days.
I hope it is clear now.

Try to solve the other case mentioned above (when A leaves 10 days before the "scheduled" completion). U will get what u had got with your method (and explanation).

CZ@@@H@@@R · Serious about CAT Joined: 14 Jan 2006 Posts: 64

For such type of problems, Moving in a "REVERSE GEAR" is the easiest way.

If 18 has to be answer. Then A worked for 8 days and B for 18 days.

Therefore 8(1/20) + 18(1/30) = 1

Hence 18 is the correct answer.

sarkar · Joined: 24 May 2006 Posts: 1

the best way to solve such problems is--
la work for x days (say)theny y for x+10 days so work don by them is equal to 1
mathematically,
(x/20) +(x+10)/30=1

on solving it for x, we get
50x+200=600,
50x=400 so x=8
so total days of work is x+10
that is 18

so the answer is 18