Question: A water tank is fitted with 8 pipes, some of these 8 pipes fill the tank and others empty the tank. Each of the pipes that fills the tank fills it in 8 hours, while each of the pipes that empties the tank empties it in 6 hours. If all the 8 pipes are kept open when the water tank is full, it takes 6 hours to drain the tank. How many of these 8 pipes fill the tank?

1. 2 pipes
2. 4 pipes
3. 5 pipes
4. 6 pipes
5. 8 pipes

Correct Answer: B
Solution and Explanation:
Approach Solution 1: 

We have been given that the Total number of pipes = 8
As each of the pipes filling the tank takes 8 hours to fill it, the Rate of Inlet = 1/8
Similarly, each of the pipes that empties the tank empties it in 6 hours. Thus, the Rate of outlet= 1/6
Consider that the total volume of the tank= LCM(6,8)=24 liters

Rate of filling = 24/8 = 3 liters/hour,
and Rate of draining =24/6 = 4 liters/hour

If, the Total number of Inlet pipes= x
Total number of outlet pipes = 8-x

We know that if all the 8 pipes are kept open when the water tank is full, it takes 6 hours to empty the tank, thus using this statement and the above calculations, we get:

Therefore, {(8-x)*4 - 3x}*6= 24
32 – 4x – 3x = 4
Thus, x = 4

Hence, the total number of inlet pipes = 4.

Approach Solution 2:

We have been given that the Total number of pipes = 8
As each of the pipes filling the tank takes 2 hours to fill it, the Rate of Inlet = ½
Similarly, each of the pipes that empties the tank empties it in 1.5 hours, the Rate of outlet= 1/.1
Consider that the total volume of the tank= LCM(1.5,2)=6 liters

Rate of filling = 6/2 = 3 liters/hour,
and Rate of draining =6/1.5 = 4 liters/hour

If, the Total number of Inlet pipes= x
Total number of outlet pipes = 8 – x

We know that if all the 8 pipes are kept open when the water tank is full, it takes 6 hours to empty the tank, thus using this statement and the above calculations, we get:

Therefore, {(8-x)*4 - 3x}*6= 24
32 – 4x – 3x = 4
Thus, x = 4

Hence, the total number of inlet pipes = 4.

Approach Solution 3:

We have been given that the Total number of pipes = 8
As each of the pipes filling the tank takes 12 hours to fill it, the Rate of Inlet = 1/12
Similarly, each of the pipes that empties the tank empties it in 9 hours, the Rate of outlet= 1/9
Consider that the total volume of the tank= LCM(9,12)=36 liters
Rate of filling = 36/12= 3 liters/hour, and Rate of draining =36/9 = 4 liters/hour

If, the Total number of Inlet pipes= x
Total number of outlet pipes = 8 – x

We know that if all the 8 pipes are kept open when the water tank is full, it takes 6 hours to empty the tank, thus using this statement and the above calculations, we get:

Thus {(8-x)*4 - 3x}*6= 24
32 – 4x – 3x = 4
Thus, x = 4

Hence, the total number of inlet pipes = 4

“A water tank is fitted with 8 pipes, some of these 8 pipes fill the”- is a topic of the GMAT Quantitative reasoning section of GMAT. To solve GMAT Problem Solving questions a student must have knowledge about a good amount of qualitative skills. GMAT Quant practice papers improve the mathematical knowledge of the candidates as it represents multiple sorts of quantitative problems.

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