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

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A and B can complete a work working individually in 60 days and 40 day  [#permalink]

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New post 07 Jan 2020, 05:12
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Question Stats:

65% (02:08) correct 35% (02:02) wrong based on 49 sessions

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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

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Re: A and B can complete a work working individually in 60 days and 40 day  [#permalink]

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New post 18 Jan 2020, 20:03
1
ManjariMishra wrote:
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


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.
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Re: A and B can complete a work working individually in 60 days and 40 day  [#permalink]

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New post 18 Jan 2020, 03:19
Bunuel wrote:
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



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.
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A and B can complete a work working individually in 60 days and 40 day  [#permalink]

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New post Updated on: 19 Jan 2020, 23:21
1
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.
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Originally posted by svasan05 on 18 Jan 2020, 05:36.
Last edited by svasan05 on 19 Jan 2020, 23:21, edited 1 time in total.
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Re: A and B can complete a work working individually in 60 days and 40 day  [#permalink]

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New post 18 Jan 2020, 12:58
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
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Re: A and B can complete a work working individually in 60 days and 40 day  [#permalink]

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New post 18 Jan 2020, 20:54
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)
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Re: A and B can complete a work working individually in 60 days and 40 day  [#permalink]

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New post 19 Jan 2020, 06:40
Chose C - logic was:
Total days: X
So:
4*(1/60)+(1/60+1/40)(X-4)=1
X = 26.4
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Re: A and B can complete a work working individually in 60 days and 40 day   [#permalink] 19 Jan 2020, 06:40
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