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20 Aug 2022, 18:18
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B
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
65%
(hard)
Question Stats:
65% (02:56) correct
35%
(03:08)
wrong
based on 218
sessions
History
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Two pipes A and B are attached to an empty water tank. Pipe A fills the tank while pipe B drains it. If pipe A is opened at 2 pm and pipe B is opened at 3 pm, then the tank becomes full at 10 pm. Instead, if pipe A is opened at 2 pm and pipe B is opened at 4 pm, then the tank becomes full at 6 pm. If pipe B is not opened at all, then the time, in minutes, taken to fill the tank is
A. 128
B. 144
C. 180
D. 240
E. 256
Source : Wizako
A. 128
B. 144
C. 180
D. 240
E. 256
Source : Wizako
G-Man
Joined: 01 Apr 2022
Last visit: 28 Jun 2024
Posts: 47
Given Kudos: 56
Location: India
Schools: ISB '25 (I) IIMA '25 (A)
GMAT 1: 690 Q50 V34
GMAT 2: 730 Q49 V40
GPA: 4
Products:
Let Va be the time taken by pipe A to fill the tank and Vb for pipe B.
Rate of Pipe A = 1/Va
Rate of pipe B = 1/Vb
Consider case 1
8/Va - 7/Vb = 1 (Eq.2)
Consider case 2
4/Va - 2/Vb = 1 (Eq.2)
4Vb = 5Va ---> Vb = 5/4 Va
Substituting in equation 1
12/(5*Va) = 1
Implies = 12/5 hrs at Va rate will fill the tank
12/5*60 = 144 minutes.
Answer is B
Rate of Pipe A = 1/Va
Rate of pipe B = 1/Vb
Consider case 1
8/Va - 7/Vb = 1 (Eq.2)
Consider case 2
4/Va - 2/Vb = 1 (Eq.2)
4Vb = 5Va ---> Vb = 5/4 Va
Substituting in equation 1
12/(5*Va) = 1
Implies = 12/5 hrs at Va rate will fill the tank
12/5*60 = 144 minutes.
Answer is B
30 Aug 2022, 17:22
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As we know,
Work = Rate x Time
Hint: Work is always 1 in such scenario (i.e. filling a water tank)
Now, suppose A takes A hours to fill the complete tank when working alone, and B takes B hours to do the same job working alone. So, rate of A becomes 1/A and that of B becomes 1/B
When B starts draining at 3PM:
1 = [{(Rate of A working alone from 2PM to 3PM x 1 Hour from 2PM to 3PM)} + {(Combined Rate of A and B working together from 3PM to 10PM) x (7 hours Combined time from 3PM to 10PM)}]
1 = [(1/A x 1) + (1/A - 1/B) x 7] (As A fills the water and B drains out, so combined rate = Rate of A - Rate of B)
1 = 1/A + 7/A - 7/B
1= 8/A - 7/B ---------- (Eq. 1)
Similarly, when B starts draining at 4PM:
1 = [{(Rate of A working alone from 2PM to 4PM x 2 Hour from 2PM to 4PM)} + {(Combined Rate of A and B working together from 4PM to 6PM) x (2 hours Combined time from 4PM to 6PM)}]
1 = [(1/A x 2) + (1/A - 1/B) x 2]
1 = 2/A + 2/A - 2/B
2 = 4/A - 2/B --------- (Eq. 2)
After solving (Eq. 1) and (Eq. 2) simultaneously (i.e. multiplying (Eq. 1) by 2 on both sides and multiplying (Eq. 2) by 7 on both sides to make coefficients of variable B same:
(Eq. 2) becomes: 7 = 28/A - 14/B
(Eq.1) becomes: 2 = 16/A - 14/B
After subtracting (Eq. 1) from (Eq. 2):
5 = 12/A - 0
So, A = 12/5 hours = 12/5 x 60 minutes = 144 minutes Answer!
Hence, Choice B must be correct!
Work = Rate x Time
Hint: Work is always 1 in such scenario (i.e. filling a water tank)
Now, suppose A takes A hours to fill the complete tank when working alone, and B takes B hours to do the same job working alone. So, rate of A becomes 1/A and that of B becomes 1/B
When B starts draining at 3PM:
1 = [{(Rate of A working alone from 2PM to 3PM x 1 Hour from 2PM to 3PM)} + {(Combined Rate of A and B working together from 3PM to 10PM) x (7 hours Combined time from 3PM to 10PM)}]
1 = [(1/A x 1) + (1/A - 1/B) x 7] (As A fills the water and B drains out, so combined rate = Rate of A - Rate of B)
1 = 1/A + 7/A - 7/B
1= 8/A - 7/B ---------- (Eq. 1)
Similarly, when B starts draining at 4PM:
1 = [{(Rate of A working alone from 2PM to 4PM x 2 Hour from 2PM to 4PM)} + {(Combined Rate of A and B working together from 4PM to 6PM) x (2 hours Combined time from 4PM to 6PM)}]
1 = [(1/A x 2) + (1/A - 1/B) x 2]
1 = 2/A + 2/A - 2/B
2 = 4/A - 2/B --------- (Eq. 2)
After solving (Eq. 1) and (Eq. 2) simultaneously (i.e. multiplying (Eq. 1) by 2 on both sides and multiplying (Eq. 2) by 7 on both sides to make coefficients of variable B same:
(Eq. 2) becomes: 7 = 28/A - 14/B
(Eq.1) becomes: 2 = 16/A - 14/B
After subtracting (Eq. 1) from (Eq. 2):
5 = 12/A - 0
So, A = 12/5 hours = 12/5 x 60 minutes = 144 minutes Answer!
Hence, Choice B must be correct!
