Question 1. Pipes A and B can fill a tank in 5 and 6 hours respectively. Pipe C can empty it in 12 hours. If all the three pipes are opened together, then the tank will be filled in:
Options
A. $1\frac{13}{17}$ hrs
B. $2\frac{8}{11}$ hrs
C. $3\frac{9}{17}$ hrs
D. $4\frac{1}{2}$ hrs
Solution :
$\eqalign{ & {\text{Net}}\,{\text{part}}\,{\text{filled}}\,{\text{in}}\,{\text{1}}\,{\text{hour}} \cr & = {\frac{1}{5} + \frac{1}{6} - \frac{1}{{12}}} = \frac{{17}}{{60}} \cr & \therefore {\text{The}}\,{\text{tank}}\,{\text{will}}\,{\text{be}}\,{\text{full}}\,{\text{in}}\,\frac{{60}}{{17}}\,{\text{hours}} \cr & i.e.,\,3\frac{9}{{17}}\,{\text{hours}} \cr} $
Correct option: A
Question 1. A pump can fill a tank with water in 2 hours. Because of a leak, it took 2\frac{1}{2} hours to fill the tank. The time taken to empty the full tank due to leakage (in hours) is :
Options
A. \frac{10}{3} hrs
B. \frac{3}{10} hrs
C. \frac{4}{5} hrs
D. \frac{1}{2} hrs
Solution :
Work done by the leak in 1 hour
$\eqalign{& = {\frac{1}{2} - \frac{2}{5}} = \frac{3}{{10}} \cr}$
∴ Leak will empty the tank in \frac{10}{3} hours
Correct option: A
Question 1: Two pipes A and B can fill a tank in 15 minutes and 20 minutes respectively. Both the pipes are opened together but after 4 minutes, pipe A is turned off. What is the total time required to fill the tank?
Options
A. 10 min. 20 sec.
B. 11 min.
C. 14 min. 40 sec.
D. 12 min. 30 sec.
Solution :
$\eqalign{ & {\text{Part}}\,{\text{filled}}\,{\text{in}}\,{\text{4}}\,{\text{minutes}} \cr & = 4\left( {\frac{1}{{15}} + \frac{1}{{20}}} \right) = \frac{7}{{15}} \cr & {\text{Remaining}}\,{\text{part}} = {1 - \frac{7}{{15}}} = \frac{8}{{15}} \cr & {\text{Part}}\,{\text{filled}}\,{\text{by}}\,B\,{\text{in}}\,{\text{1}}\,{\text{minute}} = \frac{1}{{20}} \cr & \therefore \frac{1}{{20}}:\frac{8}{{15}}::1:x \cr & x = {\frac{8}{{15}} \times 1 \times 20} \cr & \,\,\,\,\,\, = 10\frac{2}{3}\,\min \cr & \,\,\,\,\,\, = 10\min .\,40\,\sec . \cr & \therefore {\text{The}}\,{\text{tank}}\,{\text{will}}\,{\text{be}}\,{\text{full}}\,{\text{in}}\, \cr & = {4\min . + 10\min . +\, 40\sec .} \cr & = 14\min .\,40\sec . \cr} $
Correct option: C