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A tank has three taps a, b and c. If a and b is open, it can fill the tank in 12 hours, If b and c is open it can fill the tank in 15 hours and if a and c is open it can fill the tank in 20 hours. If only tap a is open in how much time it will fill the entire empty tank alone.

A tank has three taps a, b and c. If a and b is open, it can fill the tank in 12 hours, If b and c is open it can fill the tank in 15 hours and if a and c is open it can fill the tank in 20 hours. If only tap a is open in how much time it will fill the entire empty tank alone. Correct Answer 30 hours

Given:

a and b can fill the tank in 12 hrs

b and c can fill the tank in 15 hrs

a and c can fill the tank in 20 hrs

Calculation:

let capacity of the tank be 60p

the efficiency of a + b = 60p / 12 = 5p      ----1

the efficiency of b + c = 60p / 15 = 4p      ----2

the efficiency of a + c = 60p / 20  = 3p      ----3

adding equation 1,2 and 3

we get, 2a + 2b + 2c = 12p

a + b + c = 6p

so, efficiency of a = 6p - 4p = 2p

Time required to fill the tank by tap a = 60p/2p

⇒ 30 hours

∴ Tap a can fill it in 30 hours

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