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Given below are two quantities named A and B. Based on the given information, you have to determine the relation between the two quantities. You should use the given data and your knowledge of Mathematics to choose between the possible answers. Two taps A and B can fill a tank in 12 hrs and 18 hrs respectively. Both taps are opened together but it was found that it took 108 minutes more to fill the tank due to leakage C at the bottom of the tank. Quantity A: If the tank is full, find the time in which the leakage would empty it. Quantity B: If the tap A works half its efficiency, tap B works 3/4th of its efficiency and leakage C drains double amount of water than earlier, then in what time an empty tank will get full?

Given below are two quantities named A and B. Based on the given information, you have to determine the relation between the two quantities. You should use the given data and your knowledge of Mathematics to choose between the possible answers. Two taps A and B can fill a tank in 12 hrs and 18 hrs respectively. Both taps are opened together but it was found that it took 108 minutes more to fill the tank due to leakage C at the bottom of the tank. Quantity A: If the tank is full, find the time in which the leakage would empty it. Quantity B: If the tap A works half its efficiency, tap B works 3/4th of its efficiency and leakage C drains double amount of water than earlier, then in what time an empty tank will get full? Correct Answer Quantity A = Quantity B or No relation.

Suppose A, B and C are the efficiencies of tap A, B and leakage C respectively;

Suppose total units of water to be filled in the tank = 36 (LCM of 12 & 18);

∴ Efficiency of tap A = 36/12 = 3

Efficiency of tap B = 36/18 = 2

∴ (A + B) = 3 + 2 = 5

∴ Time taken to fill the tank (if there is no leakage) = 36/5 = 7.2 hours = 432 minutes

∵ it was found that it took 108 minutes more to fill the tank due to leakage C;

∴ Time taken to fill the tank (if there is leakage) = 432 + 108 = 540 minutes = 9 hours

∴ (A + B – C) = 36/9 = 4

∴ Efficiency of leakage C = 5 – 4 = 1

Quantity A:

If the tank is full, time in which the leakage would empty it = 36/1 = 36 hrs

Quantity B:

∵ tap A works half its efficiency, tap B works 3/4th of its efficiency and leakage C drains double amount of water than earlier;

∴ Efficiency of tap A = 3/2 = 1.5

Efficiency of tap B = 2 × 3/4 = 1.5

Efficiency of leakage C = 1 × 2 = 2

∴ Time taken to fill the tank = 36/(1.5 + 1.5 – 2) = 36

∴ Quantity A = Quantity B

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