Problem Solving

Dear Mr. Anurag,

At first you have said to calculate 12 days is baseless. However, again you have used 12 days to find out 8 days. Can you please explain?


Cheers.

Anurag@Gurome wrote:

eyelikecheese wrote:Hey guys I'm arriving at a different answer. Can someone explain this to me.

1/20 +1/30 is 1/12 of the job/each day

So it takes 12 days to complete the job. Thus, 2 days into it, A quits.

1/6 of the job has been done in 2 days and B has 1/30 of the job for the remaining 5/6 of the job. This comes to 25 days+the original 2=27?

What am I computing wrong?

You're assuming that A and B together has completed the job in 12 days and then you are saying A has left after 2 days! That makes your initial assumption (i.e. A and B together has completed the job in 12 days) baseless! And thus A did not left after 2 days.

After how many days A left the work depends upon the total number of days it took to complete the job. Thus it's a reverse calculation problem.

A left 10 days before the project is complete.
Thus for last 10 days only B has done the work => In last 10 days B has done (10/30) = 1/3 of the project.

Thus, A and B together has done 2/3 of the project.
To do 2/3 of the project A and B together took 12*(2/3) = 8 days

Thus the number of days the project took to be completed = Number of days together A and B worked + number of days only B worked = 8 + 10 = 18

The correct answer is A.

I came to the same answer as eyelikecheese.

Combined rate of working = r(A) + r(B) = 1/20 + 1/30 = 1/12 projects per day. So if they had worked together for the entire duration, they could have completed the project in 12 days.

But A quit 10 days before the scheduled/expected completion, i.e., he worked for 2 days. In those two days, they completed 1/12 * 2 = 1/6th of the project. A quit, so B had to complete the remaining portion (5/6th of the project). Since he can complete 1 project in 30 days, he can complete 5/6th of the project in 25 days.

Total project duration = 2 + 25 = 27 days.

I am completely lost on this problem. Who has the right answer and can they provide with a step by step, easy to understand explanation? I got to where they can do it in 12 days together but after that I was lost.

sanju09 wrote: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?

A. 18 days
B. 27 days
C. 26.67 days
D. 16 days
E. 12 days

Let the total work be 60 units

Productivity of A per day is 3 units / day

productivity of B is 2 units /day


Productivity of A and B is 5 units/ day


Say they work for N days together , so they produce...

N * 5 = 5N units in N days

After that A stops and B works alone for 10 more days..

So in those 10 days B produces , 2*10 = 20 units...


Together they produce -

5N + 20 = 60

Now , 5N = 40

Hence N = 8


A and B works together for 8 days then B works alone for 10 days , so they took , 18 days for completion of the project..

B alone has worked for 10 days=1/3 part of the work.

A and B has worked (T-10)days where T is the actual time of completion after A quits.

so A and B has done (T-10)*1/12= 1-1/3
or T=18 days

ans is (A)

I think the 27days answer is correct.

Mathmatically aside, common sense would also agree to 27 days. B can finish the job in 30 days. A worked with him only for 2 days. so it was like B got kind of assistance from A for only those 2 days. Now If he is going to work without A, and at his speed, then he is going to take his time i.e. 30 days. so the answer has to be near 26-27-28 not 18.

Shabana wrote:I think the 27days answer is correct.

Mathmatically aside, common sense would also agree to 27 days. B can finish the job in 30 days. A worked with him only for 2 days. so it was like B got kind of assistance from A for only those 2 days. Now If he is going to work without A, and at his speed, then he is going to take his time i.e. 30 days. so the answer has to be near 26-27-28 not 18.

If B works for more than 10 days after A quits, then the condition that A quits 10 days before the project is completed has not been satisfied. Your line of reasoning would be appropriate if the question were as follows:

A can complete a project in 20 days. B can complete the same project in 30 days. Working together, A and B can complete the project in t days. After working with B for t-10 days, A quits, leaving B to complete the project alone. In how many days is the project completed?

For this problem, we could use the following approach:
Let the job = 60 units.
A's rate = 60/20 = 3 units per day.
B's rate = 60/30 = 2 units per day.
t = 60/(3+2) = 12 days.
Worked completed by A and B in t-10 days = (3+2)*2 = 10 units.
Time for B to complete the remaining 50 units = 50/2 = 25 days.
Total number of days to complete the project = 2+25 = 27 days.

Rastis wrote:I am completely lost on this problem. Who has the right answer and can they provide with a step by step, easy to understand explanation? I got to where they can do it in 12 days together but after that I was lost.

Hi Rastis..
You got to where they togethr can complete work in 12 days....right
A quit before 10 days means B alone worked for last 10 days...
B work for 1day= 1/30 so his work for 10 days=1/3

Left job 1- 1/3 = 2/3

Now A& B together do job in 12 day
1/12 job in 1day
2/3 job in 12 * 2/3 = 8 days

So total time to complete = 10 +8 = 18 days...

I think that it is the easiest explaination to this....

sanju09 wrote: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?

A. 18 days
B. 27 days
C. 26.67 days
D. 16 days
E. 12 days

Let the total work be 60 units

Efficiency of A is 3 units/day

Efficiency of B is 2 units/day

Let B worked for n day ( He completed the work ) , and A worked for n - 10 days..

So , total production by both of them is -

n * 2 + (n -10)*3 = 60

or, 2n + 3n -30 = 60

Or, 5n = 90

Hence n = 18


So the entire project is completed in 18 days....

My Bit.

B worked for 10 days. Then, A and B together completed the project.

B finishes 10*(1/30)= 1/3 rd of the project. ( In 1 day B does 1/30 of the project)

Rate of A+B in 1 day = 1/12 th of the project. ( A + B = 1/20 + 1/30 = 1/12)

Hence no of days to complete 2/3rd of project = 2/3 * 12 = 8 days

Total days = 10+8= 18.

(A)

sanju09 wrote: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?

A. 18 days
B. 27 days
C. 26.67 days
D. 16 days
E. 12 days

It depends on how you interpret "10 days before the project is completed" - are we saying 10 days before it is supposed to be completed on the normal project timeline, or 10 days before it is actually completed in real life? Let's say the whole project has 60 units of work. A working alone does 3 units/day and B working alone does 2 units/day. A and B working together do 5 units/day.

If they are working together, they'd plan to work for (60/5=) 12 days. A quits with 10 days remaining = after 2 days, with 10 units done and 50 remaining. B completes the remaining 50 in 25 days at 2 units/day. So answer is B. 2 + 25 = 27 days.

However, if we're saying A quit 10 days before the project was completed rather than 10 days before it was scheduled to be completed (subtle difference), then B worked alone for 10 days and did 20 units, while A and B did the other 40 units together in 8 days. So answer is A. 10 + 8 = 18 days.

I'm inclined towards A. 18, but I can see why B. 27 looks reasonable as well.

You CANNOT take this approach to find the total no. of days required to complete the job
1/20+1/30=1/12 per day.
This approach would have been fine, if A did not quit the job 10 days before the completion of job.
If you do like this, then after A quits in 2 days B WILL NOT be able to complete the job in next 10 days. Take a look below:

Let total work = 60 units
A = 3 units/day
B = 2 units/day

If A quits after 2 days, then work done in 2 days = (3+2)*2 units = 10 units
Remaining work = 50 units
To complete 50 units of work B will take (50/2) days = 25 days.
Hence total days required to complete the job in this case = 27 days.
Now, if A quits after 2 days of work, then he is quitting 25 DAYS before completion of work and not 10 days.
Hence this approach is flawed!

Correct way would be to assume that the work is completed in say 'x' days.
A works for 'x-10' days and B works for 'x' days
Therefore 3(x-10)+2x=60
5x=90
x=18
So 18 is the correct answer. You can cross check it also if you want.

The trick is that it is given that A quits 10 days before end of the project, hence we have to assume that the time taken by the project to complete s x days and then solve.

the best explanation.thank you!

Abhishek009 wrote:

sanju09 wrote: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?

A. 18 days
B. 27 days
C. 26.67 days
D. 16 days
E. 12 days

Let the total work be 60 units

Efficiency of A is 3 units/day

Efficiency of B is 2 units/day

Let B worked for n day ( He completed the work ) , and A worked for n - 10 days..

So , total production by both of them is -

n * 2 + (n -10)*3 = 60

or, 2n + 3n -30 = 60

Or, 5n = 90

Hence n = 18


So the entire project is completed in 18 days....