A tank is filled in 8 hours by three inlet pipes K, L and M. Pipe K is twice as fast as pipe L, and pipe L is twice as fast as pipe M. If only pipe L is opened, how many hours will it take to fill the tank?

Introduction / Context:
This is another work and time question involving three pipes with different speeds. The ratio relationships are given in terms of speed, and we know the combined time to fill the tank. The problem then asks for the time taken by one intermediate speed pipe alone. This tests the ability to translate verbal statements about relative speed into algebraic rates, combine them correctly, and then invert the rate to obtain time.

Given Data / Assumptions:

Three inlet pipes K, L and M together fill the tank in 8 hours.

K is twice as fast as L.

L is twice as fast as M.

Flow rates are constant and there are no leaks.

Concept / Approach:
The main strategy is identical to similar ratio work problems. Define the slowest rate as a variable and express the others as multiples of it. Sum the three rates to match the given combined time, and then solve for the individual rate of the pipe of interest. Since time is the reciprocal of rate for one unit of work, once the rate is known, the time follows directly. Using hours coherently throughout avoids unit mistakes.

Step-by-Step Solution:
Let the rate of the slowest pipe M be r tanks per hour.Given that L is twice as fast as M, the rate of L is 2r tanks per hour.Given that K is twice as fast as L, the rate of K is 2 * 2r = 4r tanks per hour.Therefore, the combined rate of K, L and M is r + 2r + 4r = 7r tanks per hour.Together they fill the tank in 8 hours, so 7r = 1/8 tank per hour.Thus r = 1 / (8 * 7) = 1/56 tank per hour.The rate of L is 2r = 2/56 = 1/28 tank per hour.Therefore, the time taken by L alone to fill the tank is 1 / (1/28) = 28 hours.
Verification / Alternative check:
Check with the computed rates: M = 1/56, L = 1/28, K = 1/14 tank per hour.Combined rate = 1/56 + 1/28 + 1/14.Convert to a common denominator of 56: 1/56 + 2/56 + 4/56 = 7/56 = 1/8 tank per hour.Time to fill one tank at this rate is 8 hours, which agrees with the statement.
Why Other Options Are Wrong:
24 hours and 28 hours are close but only 28 hours exactly matches the required combined time when used to derive the correct rates. Values like 32, 36 and 40 hours would lead to rates for L that are too slow or too fast and would no longer give a combined filling time of 8 hours when combined with the other pipes according to the given ratios.

Common Pitfalls:
It is easy to misassign the ratios, for example saying K : L : M = 1 : 2 : 4 instead of 4 : 2 : 1. Another frequent error is to forget that the combined rate is the sum of the individual rates, and instead average the given times directly, which does not work in such problems. Some students also mix up which pipe is twice as fast as which and end up with inverted ratios. Carefully reading that K is twice as fast as L and that L is twice as fast as M is crucial for building the correct expressions.

Final Answer:
Pipe L alone will fill the tank in 28 hours.