9 taps are filled to a water tank. Some of them are water taps to fill the tank and remaining are outlet taps are used to empty the tank. Each inlet tap can fill the tank in 9 hours and each outlet tap can empty the tank in 9 hours. On opening all the taps, the tank is filled in 9 hours. Find the number of inlet water taps.
Answers
Step-by-step explanation:
Total number of taps = 9
Time taken by each inlet tap to fill the tank = 20 hours
Time taken by each outlet tap to empty the tank = 30 hours
Total time taken to fill the tank = 5 hours
Concept used:
Total work = Time taken × Efficiency
And, Total efficiency = efficiency of inlet taps – efficiency of outlet taps
Calculation:
Let total number of inlet taps be x
Total number of outlet taps be (9 – x)
L.C.M of 20 and 30 = 60 units = Total work
Total time taken to fill the tank = 5 hours
Efficiency of all 9 taps = 60/5 = 12 units
Efficiency of each inlet tap = 60/20 = 3 units
Now, Efficiency of x inlet taps = 3x
Efficiency of each outlet tap = 60/30 = 2 unit
Efficiency of (9-x) outlet taps = (18 - 2x)
So, Total efficiency of 9 taps = efficiency of inlet taps – efficiency of outlet taps
⇒ Total efficiency of 9 taps = 2x – (18 – 2x)
So, 3x – (18 – 2x) = 12
⇒ 5x – 18 = 12
⇒ 5x = 30
⇒ x = 6
⇒ Outlet taps = (9 – 6) = 3
∴ The number of outlet taps is 3
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