Given: A, B, C are three taps connected to a tank such that 6 times the time taken by A to fill the tank is 7 times the time taken by B and C together to fill the tank. 3 times the time taken by C to fill the tank is 10 times the time taken by A and B together to fill the tank.
Asked: If A, B and C together fill the tank in 60/13 hours, then find the time taken by B alone to fill the tank?
Let the time taken by taps A, B & C be x, y & z hours respectively
6 times the time taken by A to fill the tank is 7 times the time taken by B and C together to fill the tank.
6x = 7yz/(y+z)
7/x = 6(1/y + 1/z)
3 times the time taken by C to fill the tank is 10 times the time taken by A and B together to fill the tank.
3z = 10xy/(x+y)
10/z = 3(1/x + 1/y)
A, B and C together fill the tank in 60/13 hours
1/x + 1/y + 1/z = 13/60
7/x = 6(1/y + 1/z) = 6(13/60 - 1/x) = 13/10 - 6/x
13/x = 13/10
x = 10 hours
10/z = 3(1/x + 1/y) = 3(13/60 - 1/z) = 13/20 - 3/z
13/z = 13/20
z = 20 hours
1/10 + 1/y + 1/20 = 13/60 = 3/20 + 1/y
1/y = 13/60 - 3/20 = 4/60 = 1/15
y = 15 hours
IMO B
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Kinshook Chaturvedi
Email: kinshook.chaturvedi@gmail.com