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Jay and Anup can do a job, each working alone in 30 and 15 days respec

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Bunuel
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Jay and Anup can do a job, each working alone in 30 and 15 days respec [#permalink] New post   03 Dec 2020, 01:15
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Jay and Anup can do a job, each working alone in 30 and 15 days respectively. Jay started the work and after a few days, Anup joined him. They completed the work in 18 days from the start. After how many days did Anup join A?

A. 6

B. 10

C. 12

D. 14

E. 15
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C
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Jay and Anup can do a job, each working alone in 30 and 15 days respec [#permalink] New post   03 Dec 2020, 21:55
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We know ,
Jay takes 30 days to finish a work and Anup takes 15 days.
Let's take the LCM, which is 30.
Assume there are 30 units of work to be completed.
Hence, rate of doing work for Jay would be 30/30= 1 ( rate= total workdone/total timetaken)
Similarly rate of doing work for Anup would be 30/15 = 2

Let x be the number of days Jay worked for before Anup joined.
therefore , 18-x would be the days they worked together.
We know , work done = rate * time taken
SO, total work done = work done by jay + combined work done by both
i.e 30= 1*x + 3*(18-x)
Solving for x , we get x=12.

Hence Jay works for 12 days before Anup joins in.

Edit : It's my first post , hope it fits the GMAT club standard , please share some kudos if you liked it :)
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Re: Jay and Anup can do a job, each working alone in 30 and 15 days respec [#permalink] New post   04 Dec 2020, 01:12
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Rate of Jay = 1/30
Rate of Arup = 1/15

Jay worked the whole 18 days,
Hence work done => W = R* T => W = 1/30 *18 (Do not cancel anything will help in calculation further)

Let Arup joined after x days, hence days he worked = 18-x
Work done = 18-x/15.

Total Work Done is 1
1 = Work done by Jay + Work done by Arup

X= 12 Days
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Re: Jay and Anup can do a job, each working alone in 30 and 15 days respec [#permalink] New post   03 Dec 2020, 22:24
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CONCEPT:-Time and Work
-Total work is a sum of the individual works and the collectove work(Jay and Anup here)

SOLUTION: Let the total work be LC(15,30)=30 units.
Efficiency of Jay is 1units/day and that of Anup is 2 units/day.
Together, the efficiency is (1+2)=3 units/day
Let Jay worked for "x" days alone.
Then, 1*(x) X (18-x)*3=30
=>x=12 days (C)

Hope this helps :thumbsup:
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Re: Jay and Anup can do a job, each working alone in 30 and 15 days respec [#permalink] New post   04 Dec 2020, 00:45
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Rate of Jay and Anup
1/30 & 1/15

Total work done= 1
Work done by Jay 18/30= 3/5
Work done by Anup 1-3/5= 2/5----(1)

Anup worked for x days along with Jay
So, work done by Anup = x/15-----(2)

From 1 & 2

2/5=x/15
x= 6
Jay worked alone= Total days- Anup & Jay worked together.
Jay worked alone 18-6= 12 days

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Re: Jay and Anup can do a job, each working alone in 30 and 15 days respec [#permalink] New post   03 Nov 2023, 02:51
Hello from the GMAT Club BumpBot!

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Re: Jay and Anup can do a job, each working alone in 30 and 15 days respec [#permalink]
03 Nov 2023, 02:51
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