Two pipes a and b can separately fill a tank in 2 minutes and 15 minutes respectively. both the pipes are opened together but 4 minutes after the start the pipe a is turned off. how much time will it take to fill the tank

Two pipes a and b can separately fill a tank in 2 minutes and 15 minutes respectively. both the pipes are opened together but 4 minutes after the start the pipe a is turned off. how much time will it take to fill the tank

A). 9 min

B). 10 min

C). 11 min

D). 9.5 min

Let the capacity of the tank be $ 1 $ unit.

Pipe $ A $ can fill the tank in $ 2 $ minutes, so its rate of filling is:

$ \frac{1}{2} $ tank per minute.

Pipe $ B $ can fill the tank in $ 15 $ minutes, so its rate of filling is:

$ \frac{1}{15} $ tank per minute.

Both pipes are opened together for the first $ 4 $ minutes. The part of the tank filled in $ 4 $ minutes is:

$ 4 \times \left( \frac{1}{2} + \frac{1}{15} \right) $

$ = 4 \times \left( \frac{15 + 2}{30} \right) $

$ = 4 \times \frac{17}{30} = \frac{68}{30} = \frac{34}{15} $.

After $ 4 $ minutes, pipe $ A $ is turned off, and only pipe $ B $ continues to fill the tank.

The remaining part to be filled is:

$ 1 - \frac{34}{15} = \frac{15}{15} - \frac{34}{30} = \frac{11}{30} $.

Time taken by pipe $ B $ to fill the remaining part:

$ \frac{\frac{11}{30}}{\frac{1}{15}} = \frac{11}{30} \times 15 = \frac{11}{2} = 5.5 $ minutes.

Total time to fill the tank:

$ 4 + 5.5 = 9.5 $ minutes.

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