Question

A cistern can be filled by a tap in $4$ hours while it can be emptied by another tap in $9$ hours. If both the taps are opened simultaneously then after how much time will the cistern get filled ?

• A. $4.5$ hrs
• B. $5$ hrs
• C. $6.5$ hrs
• D. $7.2$ hrs

Answer 1

Answer: (D)

$7.2$ hrs

A cistern can be filled by a tap in $4$ hours while it can be emptied by another tap in $9$ hours.

Let tap $A$ fill the cistern and tap $B$ empty the cistern.

Work done by tap $A$ $=\frac{1}{4}$

Work done by tap $B$ $=\frac{1}{9}$

Work done to fill the tap when both are opened $=\frac{1}{4}-\frac{1}{9}$

$=\frac{9-4}{36}$

$=\frac{5}{36}$

Thus, time taken to completely fill the cistern $=\frac{36}{5}$ $=7.2$ hrs