A Leak in the Bottom of a Tank can Empty the Full Tank in 6 hours GMAT Problem Solving

Question: A leak in the bottom of a tank can empty the full tank in 6 hours. An inlet pipe fills water at the rate of 4 liters a minute. When the tank is full, the inlet is opened and due to the leak, the tank is empty in 8 hours. Find the capacity of the tank:

A. 5780 liters
B. 5770 liters
C. 5760 liters
D. 5750 litres
E. 5790 liters

Correct Answer: C

Solution and Explanation:

Approach Solution 1:
The problem statement states that:
Given:

• The tank gets emptied in 6 hours.
• The Inlet pipe fills at the rate of 4 litres a minute
• If the tank is full, the inlet is opened and due to the leak, the tank is empty in 8 hours

Find out:

• the capacity of the tank. 

As given in the question leak empties 1 tank in 6 hrs. 
Therefore, the rate of work of leak = -1/6 (because it is negative work)

Inlet + leak empty the tank in 8 hrs. 
So the rate of inlet + rate of leak = -1/8 (again overall work is negative)

Rate of inlet - ⅙ = -⅛
Rate of inlet = (1/24)th tank per hour

Time taken to fill the tank by the inlet = 24 hrs

Rate of inlet = 4 lts per min = 4*60 lts per hour = 240 lts per hour

Volume of water filled in 24 hrs = 240 * 24 = 5760 lts
Hence the capacity of the tank is 5760 litres.

Approach Solution 2:
The problem statement states that:
Given:

• The tank gets emptied in 6 hours.
• The Inlet pipe fills at the rate of 4 litres a minute
• If the tank is full, the inlet is opened and due to the leak, the tank is empty in 8 hours

Find out:

• the capacity of the tank.

We can let N = the number of liters of water in the tank when it’s full. 
Therefore, the rate of the leak (without any inlet pipe filling the tank) is:
N/(60 x 6) = N/360 liters per minute. 

However, with the inlet pipe filling the tank at 4 liters per minute, the rate of the leak is:

N/(60 x 8) = N/480 liters per minute. 

Therefore, we can create the equation:

N/360 - 4 = N/480

Multiply both sides by 1440, we have:

4N - 5760 = 3N

N = 5760

Approach Solution 3:
The problem statement states that:
Given:

• The tank gets emptied in 6 hours.
• The Inlet pipe fills at the rate of 4 litres a minute
• If the tank is full, the inlet is opened and due to the leak, the tank is empty in 8 hours

Find out:

• the capacity of the tank

Let’s assume the capacity of the tank is 'x' liters.
Therefore, Inflow (inlet pipe): 240 liters per hour (since the rate of inlet = 4 lts per min = 4*60 lts per hour = 240 lts per hour)
Outflow (Leak): x/6 liters per hour
Net Outflow (Outflow - Inflow): (x/6 - 240) liters per hour
Therefore, the total outflow in 8 hours is 8(x/6 - 240) liters which is the water the tank contains since it empties in 8 hours.
Therefore,  x= 8(x/6 - 240)
Thus the capacity of the tank = x = 5760 liters

”A leak in the bottom of a tank can empty the full tank in 6 hours”- is a topic of the GMAT Quantitative reasoning section of the GMAT exam. GMAT Problem Solving questions examine the numerical literacy and calculative aptitudes of the candidates to solve mathematical problems. GMAT Quant Practice Papers provide several types of questions that help to intensify the calculative proficiency of the candidates.

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