Exercise : 6


1. A pipe can fill a tank in 15 minutes and another one in 10 minutes. A third pipe can empty the tank in 5 minutes. The first two pipes are kept open for 4 minutes in the beginning and then the third pipe is also opened. In what time will the tank be empited ?
(a) 35 min
(b) 15 min
(c) 20 min
(d) Cannot be emptied
(e) None of these
Ans.c

Proportion of the volume of the tank filled by both the

pipes in 4 min = 4(115 + 110) = 23rd of the tank

Volume of the tank filled by all the pipes working together = 115 + 110 - 15 = -130

i.e. 130 tank is emptied in 1 min.

23 rd of the tank can be emptied in \(\frac{2 \times 30}{3} = 20 \; min \)

2. Two fill pipes A and B can fill a cistern in 12 and 16 minutes respectively. Both fill pipes are opened together, but 4 minutes before the cistern is full, one pipe A is closed. How much time will the cistern take to fill ?
(a) 917min.
(b) 313min.
(c) 5 min.
(d) 3 min.
(e) None of these
Ans.a

Let cistern will be full in x min. Then,

part filled by B in x min + part filled by A in (x – 4)min = 1

\(\frac{x}{16} + \frac{x - 4}{12} = 1\)

⇒ x = 647 = 917 hours.

3. Two fill taps A and B can separately fill a cistern in 45 and 40 minutes respectively. They started to fill a cistern together but tap A is turned off after few minutes and tap B fills the rest part of cistern in 23 minutes. After how many minutes,was tap A turned-off?
(a) 9 min
(b) 10 min
(c) 12 min
(d) 7 min
(e) None of these
Ans.a

Let A was turned off after x min. Then,

cistern filled by A in x min + cistern filled by B in (x + 23) min = 1

\(\frac{x}{45} + \frac{x + 23}{40} = 1\)

⇒ 17x + 207 = 360 ⇒ x = 9 min.

4. Three fill pipes A, B and C can fill separately a cistern in 3, 4 and 6 minutes respectively. A was opened first. After 1 minute, B was opened and after 2 minutes from the start of A, C was also opened. Find the time when the cistern will be full ?
(a) 219 min.
(b) 412 min.
(c) 334 min.
(d) 3 min.
(e) None of these
Ans.a

Let cistern will be full in x min. Then,

part filled by A in x min + part filled by B in (x – 1) min + part filled by C in (x – 2)min = 1

\(\frac{x}{3} + \frac{x - 1}{4} + \frac{x - 2}{6} = 1\)

⇒ 9x = 19 ⇒ x = 199 = 219 min.

5. A tap can fill a tank in 16 minutes and another can empty it in 8 minutes. If the tank is already 1/2 full and both the taps are opened together, will the tank be filled or emptied? How long will it take before the tank is either filled or emptied completely as the case may be ?
(a) Emptied; 16 min
(b) Filled; 8 min
(c) Emptied; 8 min
(d) Filled; 12 min
(e) None of these
Ans.c

If both the pumps are opened together, then the tank will be emptied because the working efficiency of pump empting is more than that of the pump filling it. Thus in 1 min net proportion of the volume of tank filled

= (18 - 116) = 116

or the tank will be emptied in 16 min

12 tank will be emptied in 8 min.