PSA_LEVEL-UP_QNR20 . A tank has 3 inlets A,B and C and 1 outlet D. C fills the tank in one-fourth the time taken by A to fill the tank completely and in half the time taken by B to fill the tank completely. Also, the time taken to fill the tank completely by inlet C is three-fourth the time taken by D to empty the full tank completely. If D takes 6 hours to empty the full tank completely how much time (in hours) will it take to fill the empty tank if all of them are opened simultaneously?
(i) 2 hours
(ii) 3 hours 25 minutes
(iii) 4 hours 30 minutes
(iv) 4 hours 40 minutes
If D takes 6 hours to empty the full tank, C will take ¾th the time or ¾*6 or 9/2 hours to fill the tank completely alone.
Thus, A will take 4 times the time that C takes to fill it alone or 4*9/2 = 18 hours.
And B will take twice the time that C takes to fill it alone or 2*9/2 = 9 hours.
Thus the individual times for A, B, C and D are 18, 9, 9/2 and 6 hours respectively.
Let us assume, the tank’s capacity is 36 liters.
In one hour,
A will fill in 36/18 or 2 liters.
B will fill in 36/9 or 4 liters.
C will fill in 36/(9/2) or 8 liters.
D will pour out 36/6 or 6 liters.
Thus, in one hour, volume of the tank filled in= 2+4+8-6 = 8 liters.
∴ to fill 36 liters time required = 36/8= 4.5 hours. Option (iii)