• Three taps are fitted in a cistern. The empty cistern is filled by the first and the second taps in 3 and 4 h, respectively. The full cistern is emptied by the third tap in 5 h. If all three taps are opened simultaneously, the empty cistern will be filled up in
 A) $$\Large 1\frac{14}{23}$$ B) $$\Large 2\frac{14}{23}$$ C) 2 h 40 min D) 1 h 56 min

 B) $$\Large 2\frac{14}{23}$$

Part of tank filled by first tap in 1 h = $$\Large \frac{1}{3}$$

Part of tank filled by second tap in 1 h = $$\Large \frac{1}{4}$$

Part of tank emptied by third tap in 1 h = $$\Large \frac{1}{5}$$

Part of the tank filled by all pipes opened simultaneously in 1 h

= $$\Large \frac{1}{3}$$ + $$\Large \frac{1}{4}$$ - $$\Large \frac{1}{5}$$

= $$\Large \frac{20+15-12}{60}$$ = $$\Large \frac{23}{60}$$

Time taken by all the taps to fill the tank when it is empty

= $$\Large \frac{60}{23}$$h = $$\Large 2\frac{14}{23}$$ h

##### Similar Questions
1). Pipe A can fill a tank in 30 min, while pipe B can fill the same tank in 10 min and pipe C can empty the full tank in 40 min. If all the pipes are opened together, how much time will be needed to make the tank full?
 A). $$\Large 9\frac{3}{13}$$ h B). $$\Large 9\frac{4}{13}$$ h C). $$\Large 9\frac{7}{13}$$ h D). $$\Large 9\frac{9}{13}$$ h
2). Pipes A and B can fill a tank in 5 and 6 h, respectively. Pipe C can fill it in 30 h. If all the three pipes are opened together, then in how much time the tank will be filled up?
 A). $$\Large 3\frac{3}{14}$$ h B). $$\Large 2\frac{1}{2}$$ h C). $$\Large 3\frac{9}{14}$$ h D). $$\Large 2\frac{1}{14}$$ h
3). Through an inlet, a tank takes 8 h to get filled up. Due to a leak in the bottom, it takes 2 h more to get it filled completely. If the tank is full, how much time will the leak take to empty it?
 A). 16 h B). 20 h C). 32 h D). 40 h
4). A tap can fill an empty tank in 12 h and a leakage can empty the tank in 20 h. If tap and leakage both work together, then how long will it take to fill the tank?
 A). 25 h B). 40 h C). 30 h D). 35 h
5). Three taps A, B and C together can fill an empty cistern in 10 min. The tap A alone can fill it in 30 min and the tap B alone can fill it in 40 min. How long will the tap C alone take to fill it?
 A). 16 min B). 24 min C). 32 min D). 40 min
6). Two pipes P and Q can fill a cistern in 12 and 15 min, respectively. If both are opened together and at the end of 3 min, the first is closed. How much longer will the cistern take to fill?
 A). $$\Large 8\frac{1}{4}$$ B). $$\Large 8\frac{3}{4}$$ C). 5 min D). $$\Large 8\frac{1}{2}$$
7). There are three pipes connected with a tank. The first pipe can fill $$\Large \frac{1}{2}$$ part of the tank in 1 h, second pipe can fill $$\Large \frac{1}{3}$$ part of the tank in 1 h. Third pipe is connected to empty the tank. After opening all the three pipes, $$\Large 7\frac{1}{2}$$ part of the tank can be filled in 1 h, then how long will third pipe take to empty the full tank?
 A). $$\Large \frac{8}{11}$$ B). $$\Large \frac{5}{11}$$ C). $$\Large \frac{6}{11}$$ D). $$\Large \frac{7}{11}$$