Saved Bookmarks
| 1. |
A cistern has a leak which would empty it in 8 hours. A tap is turned on, which admits 6 litres a minute into the cistern and it is now emptied in 12 hours. How many litres can the cistern hold? (a) 8000 litres (b) 8400 litres (c) 8640 litres (d) 8650 litres |
|
Answer» (c) 8640 litres Suppose the cistern holds x litres of water. The tap admits 6 litres of water in 1 minute, i.e., it admits 360 litres of water in 1hour. \(\therefore\) x litres of water can be filled in \(\frac{X}{360}\) hours. The leak would empty the tank in 8 hours. \(\therefore\) In one hour, \(\frac{1}{8}\) of the tank becomes empty. If the tap and the leak both are allowed simultaneously, then the tank becomes empty in 12 hours, i.e., \(\frac{1}{8}-\frac{360}{X}\) = \(\frac{1}{12}\) \(\Rightarrow\) \(\frac{360}{X}\) = \(\frac{1}{8}\) - \(\frac{1}{12}\) = \(\frac{3-2}{24}\) = \(\frac{1}{24}\) \(\Rightarrow\) x = (360 × 24) litres = 8640 litres. |
|