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Two pipes can fill a tank in 6 minutes and 12 minutes respectively, and a third pipe can empty the tank at the rate of 18 liters per minute. If all the pipes working together can fill the empty tank in 5 minutes, the capacity of the tank is:

Solution

✅ Correct Option: 3

The tank's capacity is CC liters.

Pipe 1 fills the tank in 6 minutes, so in 1 minute it fills C6\dfrac{C}{6} liters.

Pipe 2 fills the tank in 12 minutes, so in 1 minute it fills C12\dfrac{C}{12} liters.

Pipe 3 empties at 18 liters per minute.

All pipes together fill the empty tank in 5 minutes, so in 1 minute they fill C5\dfrac{C}{5} liters.


In 1 minute, the net filling rate is:

C6+C12−18=C5\dfrac{C}{6} + \dfrac{C}{12} - 18 = \dfrac{C}{5}


The LCM of 6, 12, and 5 is 60.

Multiplying the entire equation by 60:

60×C6+60×C12−60×18=60×C560 \times \dfrac{C}{6} + 60 \times \dfrac{C}{12} - 60 \times 18 = 60 \times \dfrac{C}{5}

10C+5C−1080=12C10C + 5C - 1080 = 12C

15C−1080=12C15C - 1080 = 12C

15C−12C=108015C - 12C = 1080

3C=10803C = 1080

C=360C = 360


The capacity of the tank is 360 litres.

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