alone, Maria can complete

[sanju09]

Working alone, Maria can complete a task in 100 minutes. Shaniqua can complete the same task in two hours. They work together for 30 minutes when Liu, the new employee, joins and begins helping. They finish the task 20 minutes later. How long would it take Liu to complete the task alone?
(A) 120 minutes
(B) 150 minutes
(C) 3 hours
(D) 4 hours
(E) 300 minutes

[Rahul@gurome]

Let Liu takes x minutes to complete the task alone.
In 1 minute Maria can complete 1/100 task.
In 1 minute Shaniqua can complete 1/120 task. [As 2 hours = 120 minutes]
In 1 minute Liu can complete 1/x task.
In 30 minutes Maria + Shaniqua can complete (1/100 + 1/120) * 30 = 11/20 task
Remaining task = 1 - 11/20 = 9/20
Hence, (1/100 + 1/120 + 1/x) * 20 = 9/20
Solving we get, x = 240 minutes = 240/60 = 4 hours

The correct answer is (D).

[harshavardhanc]

Working alone, Maria can complete a task in 100 minutes. Shaniqua can complete the same task in two hours. They work together for 30 minutes when Liu, the new employee, joins and begins helping. They finish the task 20 minutes later. How long would it take Liu to complete the task alone?
(A) 120 minutes
(B) 150 minutes
(C) 3 hours
(D) 4 hours
(E) 300 minutes

see that per minute work of M = 1 % and that of S is 1/120 = .833 % , and combined work/ min = 1.833 %

now, when L joins them after 30 mins, they would have completed (30 * 1% + 30 * 1/120 ) = 55% of the work.

remaining 45 % is done by all of them in 20 mins, hence per minute work by all of them is 2.25 %.

=> per minute work by L is 2.25 - 1.833 = .4166 % ( or .833 /2 %) or (1/120/2) = 1/240.

Hence, L takes 240 mins or 4hrs.

( knowing inverses of numbers such as 1/5 , 1/6 , 1/ 12 comes in handy in this type of sums )

[quantskillsgmat]

its easy if u take question in simple way
together m and s can do 1/100+1/120=11/600 part in 1 minutes.so in 30 minutes they can finish
(11/600) x30=11/20
remaining work=1-11/20=9/20
now 1/100+1/120+1/x=9/20 get x

[sanju09]

Let Liu takes x minutes to complete the task alone.
In 1 minute Maria can complete 1/100 task.
In 1 minute Shaniqua can complete 1/120 task. [As 2 hours = 120 minutes]
In 1 minute Liu can complete 1/x task.
In 30 minutes Maria + Shaniqua can complete (1/100 + 1/120) * 30 = 11/20 task
Remaining task = 1 - 11/20 = 9/20
Hence, (1/100 + 1/120 + 1/x) * 20 = 9/20
Solving we get, x = 240 minutes = 240/60 = 4 hours

[spoiler]The correct answer is (D).
[/spoiler]

BARBAADI-LAL ka prayog bhi kar liya karo, guru ji

consider using SPOILER too, sir

great work by the way