Question

Three taps A, B and C can fill a tank in $12,15$ and $20$ hours respectively. If A is open all the time and B and C are open for one hour each alternately, the tank will be full in.

• A. $6$ hours
• B. $6\frac{2}{3}$hours
• C. $7$ hours
• D. $7\frac{1}{2}$ hours

Answer 1

The correct option is C $7$ hours

$(A+B)$'s hour's work$=\left(\frac{1}{12}+\frac{1}{15}\right)=\frac{9}{60}=\frac{3}{20}$.
$(A+C)$'s hour's work $=\left(\frac{1}{12}+\frac{1}{20}\right)=\frac{8}{60}=\frac{2}{15}$.
Part filled in $2$hrs $=\left(\frac{3}{20}+\frac{2}{15}\right)=\frac{17}{60}$.
Part filled in $6$hrs$=\left(3\times \frac{17}{60}\right)=\frac{17}{20}$.
Remaining part $=(1-\frac{17}{20})=\frac{3}{20}$.
Noe, it is turn of A and B and $\frac{3}{20}$ part is filled by A and B in $1$ hour.
$\therefore$ Total time taken to fill the tank $=(6+1)$hrs $=7$hrs.