Tap A can fill a tank in 10 hours, tap B can fill it in 20 hours, and, an outlet, Tap C, can empty the tank in 30 hours. Each tap is opened, one by one, for exactly one hour and then closed. If the tank is 1/4th full, and the taps start working in alphabetic order (A, B, and then C), after how long will the tank begin to overflow?
Let's assume that volume of the tank - 100L
1/4 full = 25L in the tank
Tap A in 10 hours fill 100L ---> speed 1h-10L
Tap B in 20 hours fill 100L ---> speed 1h-5L
Tap C in 30 hours empty 100L ---> speed 1h-3.33L
We that taps are working in alphabetic order A, B, and then C - we take in as 1 cycle:
1-cycle: 25L+10L+5L-3.33L=36.67L (in 3h)
2-cycle: 36.67L+10L+5L-3.33L=48.34L (in 6h)
3-cycle: 48.34L+10L+5L-3.33L=60.01L (in 9h)
4-cycle: 60.01L+10L+5L-3.33L=71.71L (in 12h)
5-cycle: 71.71L+10L+5L-3.33L=83.38L (in 15h)
6-cycle: 83.38L+10L+5L-3.33L=95.08L (in 18h)
So we in 6 cycles - 18h - we filled 95.08L out of 100L of the tank.
Next turn is Tap A, we need to find out in how many minutes Tap A will fill 5L.
10L-10h ---> 5L-30min
Finally in
18h 30min tank will be 100.08L begin to overflow.
A. 6 hours 25 minutes
B. 6 hours 30 minutes
C. 18 hours 25 minutesD. 18 hours 30 minutesE. 19 hours 18 minutesD is the answer. _________________
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