GATE (GA) Textile 2019 Question Paper Solution | GATE/2019/GA/07

Question 07 (General Aptitude)

Two pipes P and Q can fill a tank in 6 hours and 9 hours respectively, while a third pipe R can empty the tank in 12 hours. Initially, P and R open for 4 hours. Then P is closed and Q is opened. After 6 more hours R is closed. The total time taken to fill the tank (in hours) is _____.

(A)13.50
(B)14.50
(C)15.50
(D)16.50
Answer / Solution

P & R open .so, part of tank filled=4(\frac{1}{6}-\frac{1}{12})=1/3

After 4 hrs P is closed and for 6 more hrs Q and R are opened so,part of tank filled=6(\frac{1}{9}-\frac{1}{12})=1/6

So. total tank filled in 10hrs=(\frac{1}{6}+\frac{1}{3})=1/2

So. remaining half part is filled by Q alone

\frac{1}{2}=\frac{t}{9} , t=4.5hrs

Total time taken to fill the tank=4+6+4.5=14.5 hrs (Ans)

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