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Question 21 : 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?

- 4 : 12 PM
- 4 : 24 PM
- 4 : 48 PM
- 4 : 36 PM

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Given that a tank is emptied everyday at a fixed time point and after that either pump A or B or both start working to fill the tank.

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.

We have to find at what time will the tank filled on thursday if both were used simultaneously all along

A is doing 3 hours less work on Wednesday which B completes in 2 hours therefore B = 1.5 A

⟹ \\frac{n}{n - 2}) = \\frac{3}{2})

⟹ 2n = 3n – 6

⟹ n = 6

A takes 6 hours and B takes 4 hours or the tank is closed at 2 pm

When they are together open

⟹ \\frac{1}{6}) + \\frac{1}{4}) = \\frac{2 + 3}{12})

⟹ Rate is \\frac{5}{12}) or they can fill the entire tank in \\frac{12}{5}) hours which is 2 hours 24 minutes

Starting from 2 pm, they fill the entire tank by 4:24 pm

Here the break through is figuring out the ratio or efficiency of the rate at which they fill is B : A = 3 : 2

The conventional way is

⟹ \\frac{n - 3}{n}) + \\frac{2}{n - 2}) = 1

n-3 hours at the rate of \\frac{1}{n}) per hour

2 hours at the rate \\frac{1}{n - 2}) per hour

Solving this we get n = 6 and we can find solution using this n.

The question is **"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?"**

Choice B is the correct answer.

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