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Quantitative Reasoning – Practice – Inlet and Outlet pipes of a tank!!!

pipes and cisterns 1

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

Ans:

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)

 

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