Three pipes A, B and C are connected to a tank. Working alone, they require 10 hours, 20 hours and 30 hours respectively. After some time, A is closed and after another 2 hours, B is also closed. C works for another 14 hours so that the tank gets filled completely. Find the time (in hours) after which pipe A was closed.

**(A)** 1

**(B)** 1.5

**(C)** 2

**(D)** 3

**Answer:** **(C)** **Explanation:** Let the capacity of the tank be LCM (10, 20, 30) = 60

=> Efficiency of pipe A = 60 / 10 = 6 units / hour

=> Efficiency of pipe B = 60 / 20 = 3 units / hour

=> Efficiency of pipe C = 60 / 30 = 2 units / hour

Now, all three work for some time, say ‘t’ hours.

So, B and C work for 2 more hours after ‘t’ hours and then, C works for another 14 hours.

=> Combined efficiency of pipe A, pipe B and pipe C = 11 units / hour

=> Combined efficiency of pipe B and pipe C = 5 units / hour

So, we have 11 x t + 5 x 2 + 14 x 2 = 60

=> 11 t + 10 + 28 = 60

=> 11 t = 60 – 38

=> 11 t = 22

=> t = 2

Therefore, A was closed after 2 hours.

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