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A tank has two inlets and an outlet. The inlets fill up the tank in 6 hours and 8 hours individually and outlet empties it in 10 hours. If the inlets are opened for an hour and closed and then all the three taps are opened together, how much time will it take to fill up remaining tank?

A tank has two inlets and an outlet. The inlets fill up the tank in 6 hours and 8 hours individually and outlet empties it in 10 hours. If the inlets are opened for an hour and closed and then all the three taps are opened together, how much time will it take to fill up remaining tank? Correct Answer 85/23 hours

GIVEN:

Two inlets can fill the tank in 6 hours and 8 hours respectively.

Outlet pipe can empty the tank in 10 hours.

CALCULATION:

Two inlets can fill the tank in 6 hours and 8 hours respectively.

⇒ Quantity of tank filled by inlet pipes in 1 hour = 1/6 + 1/8 = 7/24 units

After 1 hour all the three pipe are opened then tank filled = 1/6 + 1/8 – 1/10 = 23/120 units

Total work done by all the three pipe = 1 unit

Let the remaining tank be filled in x hours.

⇒ 7/24 + x × 23/120 = 1

⇒ x = 85/23

∴ Time taken to fill the remaining tank = 85/23 hours

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