Question

Two pipes can fill a tank in 15 hours and 4 hours, respectively, while a third pipe can empty it in 12 hours. How long (in hours) will it take to fill the empty tank if all the three pipes are opened simultaneously?

• A. 30 / 7
• B. 20 / 7
• C. 50 / 7
• D. 15 / 7

Answer 1

Answer:

A. 30 / 7

Solution:

Given:

Time to fill the tank by two pipes = 15 hours and 4 hours

Time to empty the tank by third pipe = 12 hours

Concept used:

If Pipe A take ‘x’ hours and Pipe B takes ‘y’ hours to fill a tank then assume the total capacity of the tank is equal to LCM of ‘x’ and ‘y’ or a multiple of them.

Formula used:

Efficiency = Total work/total time

Calculations:

Let the total capacity of the tank be LCM of 15, 4, and 12 i.e. 60 units.

The efficiency of the first pipe = 60/15

⇒ 4 units/hour

The efficiency of the second pipe = 60/4

⇒ 15 units/hour

The efficiency of the third pipe = 60/12

⇒ 5 units/hour

Combined efficiency of three pipes = 4 + 15 - 5

⇒ 14 units/hour

Time to empty the tank by all the pipes together = 60/14

⇒ 30/7 hours

∴ It takes 30/7 hours to fill the empty tank if all three pipes are opened simultaneously.

Shortcut Trick Total work = 60 unit

	A	B	C
Efficiency	4	15	-5

 

Total efficiency = 4 + 15 - 5 = 14

∴ Time is taken to fill the tank = 60/14 = 30/7 hours