Multiple choice

A water tank has eight pipes fitted into it. Pipes are of two types: Green Pipe and Red Pipe. Green pipes are used to fill the tank and the Red pipes are used to empty the tank. Every Green pipe can fill the tank in 12 hours and every Red pipe can empty it in 36 hours. On opening all the pipes an empty tank is filled in 3 hours. The number of Red pipes is

  1. 5

  2. 3

  3. 4

  4. 2
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Let G be the number of green pipes and R be the number of red pipes. G+R=8. The net rate is (G/12) - (R/36) = 1/3. Substituting R=8-G: (G/12) - ((8-G)/36) = 1/3. Multiplying by 36: 3G - 8 + G = 12, so 4G = 20, G=5. Thus R=3.

AI explanation

Assuming the total capacity of the tank is the least common multiple of 12 and 36, the capacity is 36 units. Let the number of green pipes be G and the number of red pipes be R, meaning G + R = 8. The filling rate of the green pipes is 36 divided by 12, equalling 3 units per hour each, and the emptying rate of the red pipes is 36 divided by 36, equalling 1 unit per hour each. The net filling rate of all 8 pipes is 3G minus 1R, and since the tank fills in 3 hours, this rate must be 36 divided by 3, which equals 12 units per hour. Substituting G with 8 minus R gives the equation 3 times (8 minus R) minus R equals 12; solving this gives 24 minus 4R equals 12, meaning R equals 3.

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