Question: Two pipes can fill the cistern in 10hr and 12 hr respectively, while the third empty it in 20hr. If all pipes are opened simultaneously, then the cistern will be filled in

1. 7.5 hr
2. 8 hr
3. 8.5 hr
4. 10 hr
5. 11 hr

Correct Answer: A
Solution and Explanation:
Approach Solution 1:
Let the capacity of the tank be LCM(10,12,20)= 120 units
Efficiency of pipe A =12 units (+filling)
Efficiency of pipe B =10 units (+filling)
Efficiency of pipe C = 6 units (-emptying)
Total parts of the tank filled in an hour 12+10-6=16 units
Hence the time taken to fill in the tank is 120/16=15/2 =7.5hrs

Approach Solution 2:
Work done by all the tanks working together in 1 hour,
⇒1/10+1/12−1/20= 2/15
Hence, tank will be filled in
15/2= 7.5 hours.

Approach Solution 3:

Pipe A     Pipe B     Pipe C (Negative work)
10 hrs     12 hrs     -20hrs

Let's assume total work is 60 units (Which is also LCM of 10,12 & 20)
Then the Work pipes would do will be=
Pipe A= 60/10 = 6 units
Pipe B= 60/12 = 5 units
Pipe C= 60/20= -3 units (Negative value because it is emptying the tank)
Therefore, total capacity of A+B+C = 6+5-3 = 8 units
Time taken to fill the cistern= 60/8 = 7.5 hours.

“Two pipes can fill the cistern in 10hr and 12 hr respectively”- 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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