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A tank is emptied everyday at a fixed time point. Immediately thereafter, either pump A or pump B or both start working until the tank is full. On Monday, A alone completed filling the tank at 8 pm. On Tuesday, B alone completed filling the tank at 6 pm. On Wednesday, A alone worked till 5 pm, and then B worked alone from 5 pm to 7 pm, to fill the tank. At what time was the tank filled on Thursday if both pumps were used simultaneously all along?

A tank is emptied everyday at a fixed time point. Immediately thereafter, either pump A or pump B or both start working until the tank is full. On Monday, A alone completed filling the tank at 8 pm. On Tuesday, B alone completed filling the tank at 6 pm. On Wednesday, A alone worked till 5 pm, and then B worked alone from 5 pm to 7 pm, to fill the tank. At what time was the tank filled on Thursday if both pumps were used simultaneously all along? Correct Answer 4 : 24 pm

Calculation:

Let T be the time, on a 24 hours clock at which the tank is empty.
Time taken by pipe A alone to fill the tank is (20 – T) hrs.
Time taken by pipe B alone to fill the tank is (18 – T) hrs.
On the other day, A fill the tank for (15 – T) hrs and B for 2 hrs.
Let A and B be the rate of works of pipe A and B respectively.
⇒ (20 - T)A = (18 - T)B = (17 - T)A + 2B ……. (I)
After calculating, we get

⇒ A/B = 2/3

∴ (20 - T)2 = (18 - T)3

⇒ T = 14 hr
Put the value of T in equation (I)

⇒ (18 - T)B = (17 - T)A + 2B

⇒ (18 - 14)3 = (17 - 14)2 + 2 × 3 = 1

⇒ Now, We can say that

⇒ (20 - T)A = 1

⇒ A = 1/6

⇒ B = 1/4
When both work simultaneously, time taken
⇒ 1/(1/6  + 1/4) = 2.4 hrs
The tank will be filled by 14 + 2.4 hrs, 16: 24 i.e. 4: 24 pm

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