Question

A drain pipe can drain a tank in 12 hours, and a fill pipe can fill the same tank in 6 hours. A total of n pipes, which include a few fill pipes and the remaining drain pipes can fill the entire tank in 2 hours. How many of the following values could n have in this case? a. 24 b. 16 c. 33 d. 13 e. 9 f. 8

• A. 12
• B. 13
• C. 5
• D. 3
• E. 2

Hint:

In pipe problems, express rates as fractions of tank per hour. For fill pipes, rate is positive; for drain pipes, rate is negative.

Answer 1

The Correct Option is D

Step 1: Understanding the Concept:
Let capacity be 12 units. Fill rate $= +2$ units/hr, Drain rate $= -1$ unit/hr.
Step 2: Key Formula or Approach:
If $x$ are fill pipes and $(n-x)$ are drain pipes:
$2x - (n-x) = \frac{12}{2} = 6$.
Step 3: Detailed Explanation:
$3x - n = 6 \implies n = 3x - 6$.
This means $n$ must be a multiple of 3.
From the list $\{24, 16, 33, 13, 9, 8\}$, the multiples of 3 are $24, 33, 9$.
Total values $= 3$.
Step 4: Final Answer:
n can have 3 of the listed values.