work rate

[AJWILL]

A person X, working alone can complete a work in 10 days. A person Y completes the same amount of work in 20 days and a person Z when working alone can complete same amount of work in 30 days. How many more days are required if all the people started working together, but X and Y leave the work after 2 days
[A] 19
20
[C] 21
[D] 22
[E] 25

[theCEO]

imo [spoiler]c if the question wanted total days. (2+19). A) since the question mentioned how much more after the two quit (19) [/spoiler]

[AJWILL]

OA A
how do i hide the answer choice?

please give a detailed solution

[theCEO]

Rates:
X = 10days/1work
y = 20days/1work
z = 30days/1work

First find time (x) for all three to finish the job (1work) if they work together:
x * (1w/10 + 1w/20 + 1/30) = 1 w
x * (11w/60) = 1w
x = 60/11 days = time for all 3 to finish job

In (60/11) days ----- 1 work is done
Therefore in 2 days ----- [2/(60/11)] * 1work = 22/60 work is done
Work left to do after 2 days = 1w - 22/60w = 38/60 w

Z takes 30 days to do 1 work
Therefore z does 38/60 work in (38/60) * 30 days = 19 days

[AJWILL]

i did it like this..


work done in 1 day = 1/10,1/20 and 1/30 by x,y and z respectively

so,work in 2 days by x,y and z -->

1/5+1/10+1/15=6/15 (total work done in 2 days)

work left= 9/15

now z's rate*time=work

1/30*d=9/15, d=9*2 = 18

CAN SOMEONE PLEASE POINT OUT WHAT AM I DOING WRONG????

[theCEO]

i did it like this..


work done in 1 day = 1/10,1/20 and 1/30 by x,y and z respectively

so,work in 2 days by x,y and z -->

1/5+1/10+1/15=6/15 (total work done in 2 days)

work left= 9/15

now z's rate*time=work

1/30*d=9/15, d=9*2 = 18

CAN SOMEONE PLEASE POINT OUT WHAT AM I DOING WRONG????

Here is your mistake
1/5+1/10+1/15=6/15

1/5 + 1/10 + 1/15 =
6/30 + 3/30 + 2/30 = 11/30

[AJWILL]

damn!! thanks

[AJWILL]

damn!! thanks