Question

Two pipes A, B can fill a tank in 24 min and 32 min respectively. If both pipes are opened simultaneously, after how much time should B be closed so that the tank is full in 18 min?

• A. 8 min
• B. 12 min
• C. 15 min
• D. 20 min

Hint:

In variable-time pipe problems, keep one pipe running the full duration and treat the other for \(t\) minutes. Add their \emph{work} (rate \(\times\) time) to equal 1 full tank.

Answer 1

The Correct Option is A

Step 1: Write filling rates.
A’s rate \(=\frac{1}{24}\) tank/min; \quad B’s rate \(=\frac{1}{32}\) tank/min. Step 2: Set up the total-fill equation.
Let B be closed after \(t\) minutes.
A works for all \(18\) minutes; B works for \(t\) minutes.
\[ 18\cdot\frac{1}{24} + t\cdot\frac{1}{32} = 1. \] Step 3: Solve for \(t\).
\[ \frac{18}{24} + \frac{t}{32} = 1 \Rightarrow \frac{3}{4} + \frac{t}{32} = 1 \Rightarrow \frac{t}{32} = \frac{1}{4} \Rightarrow t = 8 \text{ min}. \] \[ \boxed{8\ \text{minutes}} \]