A and B can complete a work working individually in 60 days and 40 day

Question

A and B can complete a work working individually in 60 days and 40 days respectively. Both start working simultaneously on the work simultaneously, but 4 days before the work is scheduled to get over, B leaves. Find the total number of days taken for the work to be completed.

A. 24
B. 25
C. 26.4
D. 28.2
E. 30

A. 24 
B. 25 
C. 26.4 
D. 28.2 
E. 30

CrackverbalGMAT · Accepted Answer

Rate of work for A (proportion of work completed per day) = 1/60
Rate of work for B (proportion of work completed per day) = 1/40

When both are working together, the rate at which work is getting completed = 1/60 + 1/40 = 1/24

Now, at this rate, the amount of time taken for the work to get completed = 1/Rate = 24 days

B leaves 4 days before the work is to be completed ie; after 20 days.

Proportion of work completed in 20 days by A and B (working together) = Rate x Time = 20 x (1/24) = 5/6

Proportion of work remaining = 1 - (5/6) = 1/6

Now, A is working alone.

Amount of time taken by A (working alone) to complete 1/6th of the work = Work /Rate = (1/6)/(1/60) = 10 days

Therefore, total amount of time for the work to get finished = Amount of time for which A and B worked together + Amount of time for which A worked alone after B left = 20 + 10 =  30 days

Hope this helps.

chetan2u · Answer

I think there is a bit of ambiguity in the question. 
4 days before the work was SCHEDULED to get over. 
Now we are not given clearly what was planned or scheduled that is - If it was given that 
Both decide to complete the work together but B leaves 4 days before scheduled time. Here total time will be combined speed that is 24 days and B will leave after 20 days and now A will do 4 days work of B too. So addl 60*4/40=6 days and hence 24+6=30.

But what you are taking is the actual scenario, that is work getting over in y days and both working together for y-4 days. And you are correct in that scenario.

But the word Scheduled has created ambiguity.

stne · Answer

Feels as though answer should be C , here's how.

A does whole work in 60 days.Last 4 days A works alone, hence in 4 days A does 1/15 of work .
 This means A and B together did 14/15 of work .
Together A and B can do the whole work in 24 days . Hence 14/15 work they can do in 22.4 days.
Total days 22.4 + 4 =26.4 
Ans- C

Unless I am missing something,Request Moderator to check the OA.Thank you.

ManjariMishra · Answer

Bunuel   chetan2u

Can you please share where I am getting wrong :

Total Work done 240

For A 1 day it will perform 4 units of work
B : for 1 day will perform 6 units of work

(6+4)y + 4 *4 = 240 
10y =240-16
y = 22.4

Total days taken taken 26.4

Jawad001 · Answer

Rate of A = 1/60
Rate o B = 1/40
Combined Rate of A and B = 1/60 +1/40 = (2+3)/120 = 5/120 = 1/24

As B leaves 4 days before the work is scheduled to get over, A will work last 4 days alone.
The works done by A alone for the last 4 day =4/60 =1/15

Remaining works done by A and B together= 1-1/15 = 14/15
The time taken by A and B together = 14/15 * 24/1 = 112/5 = 22.4

Total time = 4 +22.4 = 26.4 days(C)

PinakiRDas · Answer

Chose C - logic was:
Total days: X
So:
4*(1/60)+(1/60+1/40)(X-4)=1
X = 26.4

Ters · Answer

I got to answer C and see that there are multiple people getting C in a similar manner, would you please explain why the answer is E?

Bunuel · Answer

Have you checked this reply? https://gmatclub.com/forum/a-and-b-can- ... l#p2442604

Shwetabh54 · Answer

Answer E is correct. If you are getting C as a answer you must have done below mistake :-

When B leaves, A has to work for 4 days to complete the work ----> WRONG (A is working 10 days to complete the remaining work)

Let's understand from example -

Let, Total work = 240, then, Rate of A = 240/60 = 4 & Rate of B = 240/40 = 6
Rate of A+B = 10
If A & B both work simultaneously then their rate will be 10 and they take 24 days to complete the work ----  This is the schedule.

Now, B leaver 4 days before, as per schedule. So, Both A&B Worked till 20 days and then B left. Work done in 20 days = 20*10 = 200

Remaining work = 240 - 200 = 40
Now, A only has to work and work left is 40. Hence A will take 10 days to complete. Sum of days = 20+10 = 30 days

Main statement to consider - A is not working 4 days to complete remaining work. It will take 4 days to complete the remaining work, only if, A&B both work. But since only A has to work, it will take more days.

A and B can complete a work working individually in 60 days and 40 day

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