A pipe is filling an empty 200-litre tank at the rate of 5 litres/hr.

Question

A pipe is filling an empty 200-litre tank at the rate of 5 litres/hr. Because of a leak, it takes 80 hours more to fill the tank. What is the rate in litres/hr at which the water is leaking?

(A) 2
(B) 3
(C) 10/3
(D) 4
(E) 5

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GMATinsight · Answer

Total Time to fill a tank @5 litre/hour = 200/5 = 40 Hours

With Leak the time to fill tank = 40+80 = 120 hours

in 120 Hours the inlet fills = 120*5 = 600 litres

Excess water filled by inlet in 120 hours = 600-200 = 400

i.e. Leak empties excess water 400 litres in 120 hours

So leakage rate = 400/120 = 40/12 = 10/3 litres/hour

Answer: Option C

verydisco · Answer

The ratio of time taken with leak and without leak is 3:1 respectively. This means that the ratio of rates must be the inverse, i.e., 1:3.

We know the rate of filling the tank when it is empty, i.e., 5 litres/hr. Therefore, we get that 3k=5, and k=5/3, where k is the multiplying constant for the ratio above. Therefore, the rate of filling the tank with the leak must be 5/3 litres/hr. Therefore, the leak must be 5-(5/3) litres/hr = 10/3 litres/hr.

In this written form, it seems longer but when done mentally, it doesn't take too long.

Abhishek009 · Answer

Efficiency of the Inlet pipe is 5 , So time taken is 40 Hours

Efficiency of the Inlet and Outlet pipe is  \frac{200}{120} = 1\frac{2}{3}

Hence, Efficiency of the outlet pipe is  5 - \frac{5}{3} = \frac{10}{3}  , Answer must be (C)

ScottTargetTestPrep · Answer

We see that without the leak, it would take 200/5 = 40 hours to fill the tank. Since now it takes 80 more hours to fill the tank, it takes 120 hours to fill the tank with the leak. We can let r = the rate of the leak and create the equation:

120 (5 - r) = 200

600 - 120r = 200

400 = 120r

r = 400/120 = 40/12 = 10/3

Answer: C

Abhishek009 · Answer

Efficiency of Inlet pipe is 5 L/Hr, So Time required by inlet pipe to fill the tank is 40 Hours

Time required to fill the tank including the leakage is 120 Hrs, So COmbined efficiency of Inlet pipe & Leakage is 200/120 = 5/3

Thus, Efficiency of Leakage is 5 - 5/3 => 10/3 , Answer must be (C)

Prowess · Answer

Leakage rate be X
Speed= distance/time
(5-X)= 200/120
X=3.33

Posted from my mobile device

Abhishek009 · Answer

The time taken to fill the tank without leak is 40 hours, however, the tank due to leakage is filled up in 120 Hours...

So, in 120 Hours the inlet pipe fills up 600 litres, but due to leakage it fills up 200 litres , thus the efficiency of the outlet is 400/120= 10/3, Answer must be (C)

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A pipe is filling an empty 200-litre tank at the rate of 5 litres/hr.

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A pipe is filling an empty 200-litre tank at the rate of 5 litres/hr.

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