Pipe P is twice as fast as Q, and Q is twice as fast as R. Find the ratio of the time taken by P, Q and R to fill a cistern.

Pipe P is twice as fast as pipe Q.

Pipe Q is twice as fast as pipe R.

If a pipe is faster, it takes less time to fill a cistern. Therefore, the time taken by each pipe is inversely proportional to its speed.

Let the time taken by R to fill the cistern be T.

Since Q is twice as fast as R, the time taken by Q is:

= $$\frac{T}{2}.$$​​

Since P is twice as fast as Q, the time taken by P is:

 = $$\frac{T}{2} \times \frac{1}{2} = \frac{T}{4}.$$​​

Therefore, the time taken by P, Q, and R are $$\frac{T}{4},$$​ $$\frac{T}{2}​,$$ and T respectively.

Ratio of Time Taken by P, Q, and R:

$$\frac{T}{4} : \frac{T}{2} : T$$​ = 1 : 2 : 4.