Three pipes A, B and C were opened to fill a cistern. Working alone, A, B and C require 12, 15 and 20 minutes respectively.After 4 minutes of working together, A got blocked and after another 1 minute, B also got blocked. C continued to work till the end and the cistern got completely filled. What is the total time taken to fill the cistern ?

**(A)** 6 minutes

**(B)** 6 minutes 15 seconds

**(C)** 6 minutes 40 seconds

**(D)** 6 minutes 50 seconds

**Answer:** **(C)** **Explanation:** Let the capacity of the cistern be LCM(12, 15, 20) = 60 units.

=> Efficiency of pipe A = 60 / 12 = 5 units / minute

=> Efficiency of pipe B = 60 / 15 = 4 units / minute

=> Efficiency of pipe C = 60 / 20 = 3 units / minute

=> Combined efficiency of pipe A, pipe B and pipe C = 12 units / minute

Now, the cistern is filled with the efficiency of 12 units / minute for 4 minutes.

=> Pool filled in 4 minutes = 48 units

=> Pool still empty = 60 – 48 = 12 units

Now, A stops working.

=> Combined efficiency of pipe B and pipe C = 7 units / minute

Now, the cistern is filled with the efficiency of 7 units / minute for 1 minute.

=> Pool filled in 1 minute = 7 units

=> Pool still empty = 12 – 7 = 5 units

Now, B also stops working.

These remaining 5 units are filled by C alone.

=> Time required to fill these 5 units = 5 / 3 = 1 minute 40 seconds

Therefore, total time required to fill the pool = 4 minutes + 1 minutes + 1 minute 40 seconds = 6 minutes 40 seconds

Quiz of this Question

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