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07 Jan 2020, 06:12
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Difficulty:
55%
(hard)
Question Stats:
66% (02:04) correct
34%
(02:29)
wrong
based on 418
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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
A. 24
B. 25
C. 26.4
D. 28.2
E. 30
Updated on: 20 Jan 2020, 00:21
Originally posted by CrackverbalGMAT on 18 Jan 2020, 06:36.
Last edited by CrackverbalGMAT on 20 Jan 2020, 00:21, edited 1 time in total.
Last edited by CrackverbalGMAT on 20 Jan 2020, 00:21, edited 1 time in total.
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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.
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.
18 Jan 2020, 21:03
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ManjariMishra
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.
