Multiple choice

A cistern filled in $20$ hours by three pipes A, B and C. The pipe C is twice as fast as B and B is thrice as fast as A. How much hours will pipe A alone take to fill the tank?

  1. $200$
  2. $400$
  3. $900$
  4. $100$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Let the rate of A be x. Then B is 3x and C is 2 * 3x = 6x. Combined rate is x + 3x + 6x = 10x. Since they fill the tank in 20 hours, the total work is 10x * 20 = 200x. Pipe A alone takes 200x / x = 200 hours.

AI explanation

Let the time taken by pipe A be x hours; since B is thrice as fast as A, B takes x/3 hours, and since C is twice as fast as B, C takes x/6 hours. The sum of their individual rates equals their combined rate, so 1/x plus 3/x plus 6/x equals 1/20. Combining the fractions gives 10/x equals 1/20, which means x equals 200. Therefore, pipe A alone takes 200 hours to fill the tank.

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