A swimming pool is completely filled in 10 hours by three tankers A, B and C working together. Tanker C is twice as fast as tanker B, and tanker B is twice as fast as tanker A. If only tanker A is used, how many hours will it take to fill the swimming pool?

Introduction / Context:
This question is another example of a work and time problem involving three agents (tankers) with speeds given in ratios. The total time taken when all three work together is known, and we must determine how long the slowest tanker alone would take to fill the swimming pool. Understanding how to express the three rates in terms of a single variable and then solving for that variable is the key skill being tested.

Given Data / Assumptions:

Tankers A, B and C together fill the pool in 10 hours.

C is twice as fast as B.

B is twice as fast as A.

All tankers have constant rates of delivering water.

Concept / Approach:
The best approach is to express the rates in terms of A, the slowest tanker. If the rate of A is r pools per hour, then B and C can be expressed as multiples of r using the given relations. Their combined rate is then related to the known total filling time of 10 hours. Once r is found, the time taken by tanker A alone is simply the reciprocal of r. This is a direct application of the principle that total work done equals combined rate times time.

Step-by-Step Solution:
Let the rate of tanker A be r pools per hour.Given that B is twice as fast as A, rate of B = 2r pools per hour.Given that C is twice as fast as B, rate of C = 2 * 2r = 4r pools per hour.Combined rate of A, B and C = r + 2r + 4r = 7r pools per hour.They together fill the pool in 10 hours, so 7r = 1/10 pool per hour.Thus r = 1 / (7 * 10) = 1/70 pool per hour.Therefore, the time taken by tanker A alone to fill the pool is 1 / r = 70 hours.
Verification / Alternative check:
Check using the computed rates.Rate of A = 1/70, rate of B = 2/70 = 1/35, rate of C = 4/70 = 2/35 pools per hour.Combined rate = 1/70 + 1/35 + 2/35.Convert to denominator 70: 1/70 + 2/70 + 4/70 = 7/70 = 1/10 pool per hour.Thus they fill the pool in 10 hours, which matches the problem statement.
Why Other Options Are Wrong:
40 hours or 50 hours would make tanker A too fast; the combined rate would then exceed 1/10 pool per hour, resulting in a filling time shorter than 10 hours. 80 or 90 hours would make tanker A too slow; when combined with B and C according to the ratio, they would take longer than 10 hours to fill the pool. Only 70 hours is consistent with all given conditions.

Common Pitfalls:
Students sometimes confuse the directions of the ratios and might mistakenly set A : B : C as 1 : 2 : 4 or 4 : 2 : 1 incorrectly. It is important to interpret "C is twice as fast as B" and "B is twice as fast as A" correctly and express each rate in terms of the slowest tanker. Another mistake is averaging the times directly instead of working with rates. Remember that rates add, while times for completion do not.

Final Answer:
Tanker A alone will take 70 hours to fill the swimming pool.