Question

How long will it take to empty the tank if both the inlet pipe A and the outlet pipe B are opened simultaneously?
I. A can fill the tank in $6$ minutes.
II. B can empty the full tank in $8$ minutes.

• A. I alone sufficient while II alone not sufficient to answer
• B. II alone sufficient while I alone not sufficient to answer
• C. Either I or II alone sufficient to answer
• D. Both I and II are not sufficient to answer
• E. Both I and II are sufficient to answer

Answer 1

The correct option is E Both I and II are sufficient to answer

I. A's $1$ minute's filling work$=\frac{1}{16}$
II. B's $1$ minute's filling work$=\frac{1}{8}$
$(A+B)$'s $1$ minute's emptying work $=\left(\frac{1}{8}-\frac{1}{16}\right)=\frac{1}{16}$
$\therefore$ Tank will be emptied in $16$ minutes.
Thus, both I and II are necessary to answer the question.
$\therefore$ Correct answer is (E).