Together, Pump A and Pump B can drain a particular tank in 2 hours and

Question

Together, Pump A and Pump B can drain a particular tank in 2 hours and 24 minutes. How many hours would it take Pump A to drain the tank alone?

(1) Pump A alone can drain the tank in 2/3 the time that Pump B alone can.
(2) Pump A alone can drain the tank 2 hours faster than Pump B alone can.

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ravi1522 · Answer

Hello ,

Together, Pump A and Pump B can drain a particular tank in 2 hours and 24 minutes. How many hours would it take Pump A to drain the tank alone?

(1) Pump A alone can drain the tank in 2/3 the time that Pump B alone can.
If the time of A is 2/3 of time B then the Rate of A will be 3/2 of Rate of B 
so we can calculate the answer
Hence Sufficient 
(2) Pump A alone can drain the tank 2 hours faster than Pump B alone can.
As we know the time relative each other then we can calculate the required answer

Hence Sufficient

Correct Answer is D

Dereno · Answer

Time taken by pump A and pump B together = Ta + Tb = 2 hrs 24 minutes = 120+24 = 144 minutes.

We need to find time taken by pump A.

Statement 1:

(1) Pump A alone can drain the tank in 2/3 the time that Pump B alone can.

Ta = (2/3)* Tb

Ta : Tb = 2:3.

Time is inversely proportional to the rate.

Ra : Rb = 3:2

Total Rates = 3K + 2K = 5K

Work = Rate * Time = 5K * 144 = 720K

Time taken by A = Ta = 720K / 3K = 240 minutes = 4*60 minutes = 4 hours.

Hence,  Sufficient.

Statement 2:

(2) Pump A alone can drain the tank 2 hours faster than Pump B alone can.

Tb = Ta+(2*60) = Ta+120

Total rate ( Ra + Rb) = Work / (Ta+Tb)

= Work / 144

(1/Ta) + (1/Ta+120) = 1/144

Solving Ta = 240 = 4 hrs.

Hence,  Sufficient

Option D

ExpertsGlobal5 · Answer

Explanation:  
 
Let the time taken by pump A to drain the tank be M mins.
Let the time taken by pump B to drain the tank be N mins.
Since (Drain Rate) x (Time taken) = (Total tank volume):
Drain rate of pump A = (1/M) of total tank volume per min.
Drain rate of pump B = (1/N) of total tank volume per min.
 
Drain rate of pump A and B together = (1/M) + (1/N)
(Drain rate of pump A and B together) x (Time taken together) = Total tank volume
  x (2 hours and 24 minutes) = Total tank volume 
  x (144 minutes) = Total tank volume 
  = (1/144) of total tank volume per min (Equation I)
  We need to find whether the value of “M/60” can be determined.  
 
 Statement (1) 
 
M = (2/3)N (Equation II)
 
From Equation I and II, we have two equations with two unknown variables, which can be solved to determine the exact value of M. 
 
It is possible to determine with certainty the number of hours taken by Pump A to drain the tank alone.   Hence, Statement (1) is sufficient.  
 
 Statement (2) 
 
M = N – 120 (Equation III)
 
From Equation I and III, we have two equations with two unknown variables, which can be solved to determine the exact value of M. 
 
It is possible to determine with certainty the number of hours taken by Pump A to drain the tank alone.   Hence, Statement (2) is sufficient.  
 
  D is the correct answer choice.

Together, Pump A and Pump B can drain a particular tank in 2 hours and

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GMAT Data Sufficiency (DS) Questions

Together, Pump A and Pump B can drain a particular tank in 2 hours and

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