Question

Two pipes A and B can fill a cistern in 12 minutes and 16 minutes respectively. If both the pipes are opened together, then after how much time B should be closed so that the tank is full in 9 minutes?

• A. $3\frac{1}{2}min$
• B. 4 min
• C. $4\frac{1}{2}min$
• D. $4\frac{3}{4}min$

Answer 1

The correct option is B 4 min

Let B be closed after x minutes.
Then, Part filled by (A+B) in xmin. + Part filled by A in (9-x) min = 1.
$\therefore$ $x(\frac{1}{12}+\frac{1}{16})+(9-x)\frac{1}{12}=1$

$or\frac{7x}{48}+\frac{9-x}{12}=1$

$or7x+36-4x=48orx=4$
So, B must be close after 4 minutes.