Two pipes A and B are attached to an empty water tank

Question

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

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Official Answer

B

A. 128
B. 144
C. 180
D. 240
E. 256

Source : Wizako

GmatPoint · Accepted Answer

Let the efficiency of pipe A per hour be A and that of B be b.

In the first case, pipe A ran for 8 hours, while pipe B ran for 7 hours.

Thus, the total capacity = 8a - 7b.....(i)

In the second case, pipe A ran for 4 hours, and B ran for 2 hours.

Total capacity = 4a - 2b....(ii)

Since both (i) and (ii) represent the total capacity,

8a - 7b = 4a - 2b

4a = 5b....(iii)

Putting the value of (iii) in (i),

The total capacity = 10b - 7b = 3b

Time taken to fill the tank with B not opened = 3b/(5b/4) = 12/5 hours = 144 minutes

Thus, the correct option is B.

G-Man · Answer

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

Mubasher · Answer

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 =

1 =   (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 =

1 =  
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!

Ahamed Imtiyaz · Answer

8/A- 7/B=1.....Eq1
4/A-2/B=1......Eq2
 to solve Eq1& Eq2 then
B=3
Then A =12/5*60= 144 minutes

Posted from my mobile device

Kinshook · Answer

Given: 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.

Asked: If pipe B is not opened at all, then the time, in minutes, taken to fill the tank is

Let the time taken by pipe A to fill the tank be x hours and time taken by pipe B to empty the tank be y hours

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. 
8/x - 7/y = 1

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.
4/x - 2/y = 1

4/x = 5/y

10/y - 7/y = 1
y = 3
x = 12/5 = 12*60/5 = 144 minutes

IMO B

Vivek1707 · Answer

This question can be done quickly if rates are assumed. That helps in avoiding fractions and dealing with clean numbers

Let rate of A and B be the units of work done per hour by pipe A and pipe B respectively

Let total work be 168 units i.e LCM 7,8,6

Focus on the time each pipe is on , the following equation would hold

8A - 7B = 168 ....i
4A - 2B = 168 ....ii

Solve both to get A = 70 units of work down per hour

Hence time taken would be 168 /70 * 60 = 144 mins

Two pipes A and B are attached to an empty water tank

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Two pipes A and B are attached to an empty water tank

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