Xavier Aptitude Test 2015 Paper

(c) Assume, the cone has volume of 24 litres (or one may assume any multiple of L.C.M. of 4, 8 and 12) A (inlet pipe) = 3 litres/hr input; B (inlet pipe) = 2 litres/hr input; C (outlet pipe) = 6 litres/hr output
If all three are open for 1 hour, then 1 litre water will go out (water volume will reduce)
Volume of the cone =

1

3

πr2h
Initial volume of water = 24 litres
If the height of the water inside the cone is reduced to50%, then the volume of water inside the inverted cone
=

1

3

π(

r

2

)2(

h

2

)=

1

8

(initial volume of water) = 3 litres
If all three pipes remain open for 20 hours, then 20 litres of water should go out and 4 litres of water should be inside the cone. However, 1 litre more water has gone out. Thus, one of the inlet pipes was open for less than 20 hours. In such case either A was closed 20 minutes earlier or B was closed 30 minutes earlier.