Two pipes X and Y can fill an empty tank in 16 hours and 20 hours respectively. Pipe Z alone can empty the completely filled tank in 25 hou… — Answer & Discussion

Two pipes X and Y can fill an empty tank in 16 hours and 20 hours respectively. Pipe Z alone can empty the completely filled tank in 25 hours. Firstly both pipes X and Y are opened and after 6 hours pipe Z is also opened. What will be the total time (in hours) taken to completely fill the tank?

A80/7
B67/7
C28/3
D304/29

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CCommunity03 May 2019

Let the tank be filled in ‘a’ hrs.

Part filled by X in 1 hr. = 1/16

⇒ Part filled by X in a hrs. = a/16

Part filled by Y in 1 hr. = 1/20

⇒ Part filled by Y in a hrs. = a/20

Part emptied by Z in 1 hr. = 1/25

⇒ Part emptied by Z in (a – 6) hrs. = (a – 6)/25

Now, Total work done = 1

⇒ a/16 + a/20 – (a – 6)/25 = 1

⇒ a(1/16 + 1/20 – 1/25) = 1 – 6/25

⇒ a(29/400) = 19/25

⇒ a = 400/29 × 19/25

⇒ a = 304/29

∴ The tank will be filled in 304/29 hrs.

CCommunity20 May 2019