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Sangeeta2018
Joined: 11 Jul 2016
Last visit: 20 Jun 2018
Posts: 40
Given Kudos: 70
Location: India
Concentration: Technology, General Management
Schools: Schulich Sept 18 Intake (A)
GMAT 1: 550 Q36 V30
GPA: 3.65
WE:Information Technology (Consulting)
22 Nov 2017, 13:43
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C
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
25%
(medium)
Question Stats:
83% (02:53) correct
17%
(03:19)
wrong
based on 156
sessions
History
Date
Time
Result
Not Attempted Yet
A does a work in 8hrs, B does the same work in 16 hrs and C does it in 12hrs. A starts working and is joined by B after 2hrs. After 3hrs of working together,A leaves and C joins. How much more time will it take to complete the work if B and C continue to work until it's over?
1.12 hr
2. 15/16 hr
3.9/7 hr
4. 5 hr
5. 16 hr
Source: Experts' Global
1.12 hr
2. 15/16 hr
3.9/7 hr
4. 5 hr
5. 16 hr
Source: Experts' Global
22 Nov 2017, 15:52
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Sangeeta2018
Attachment:
wrt3.png [ 23.8 KiB | Viewed 3758 times ]
Work rates:
A's rate: \(\frac{1}{8}\)
B's rate: \(\frac{1}{16}\)
C's rate: \(\frac{1}{12}\)
rate of A + B: (\(\frac{1}{8} + \frac{1}{16}) = \frac{3}{16}\)
rate of B + C:\((\frac{1}{16} + \frac{1}{12}) = (\frac{3}{48} + \frac{4}{48}) = \frac{7}{48}\)
Segment 1 - A works alone
A works alone for two hours. rate * time = Work
\(\frac{1}{8}* 2 = \frac{1}{4}\) work finished. Work remaining: \(\frac{3}{4}\)
Segment 2: A and B work together for 3 hours
B joins A for 3 hours.
Rate of \(A + B =\frac{3}{16}\)
Work finished? rate * time = Work
\(\frac{3}{16} * 3 hrs = \frac{9}{16}\) work is finished
Work remaining?
\((\frac{3}{4}- \frac{9}{16}) = (\frac{12}{16} - \frac{9}{16}) = \frac{3}{16}\)
Work remaining: \(\frac{3}{16}\)
Segment 3: A leaves, C joins B -- how long to finish whatever work is left?
A leaves, C joins. How long for B and C to finish? \(\frac{Work}{rate} = time\)
Rate of \(B + C =\frac{7}{48}\)
\(\frac{\frac{3}{16}}{\frac{7}{48}}\) = \((\frac{3}{16} * \frac{48}{7}) = \frac{9}{7} hrs\)
Answer C
28 Aug 2019, 10:59
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Sangeeta2018
Let the total work be 48 units (LCM of 8 , 16 & 12 )
So, Efficiency of A is 6 ; Efficiency of B is 3 ; Efficiency of C is 4
Work done by A in 2 hours is 12 units, work left is 36 units.
Work done by A and B in 3 Hours is (6 + 3)*3 = 27 , Work left is 9 units
Efficiency of B and C is 7 , work left is 9 units...
So, Time required by B and C is 9/7 Hours..., Answer must be (C)
