Pipes A and B can fill a tank in 12 hours and 16 hours respectively and pipe C can empty the full ta...........

Quantitative Aptitude (CPO) Pipes&cistern

Pipes A and B can fill a tank in 12 hours and 16 hours respectively and pipe C can empty the full tank in 24 hours. All three pipes are

opened together, but after 4 hours pipe A is closed. In how many hours from the beginning the tank be filled?

This questions was previously asked in

SSC CPO 13th-March-2019-Shift-1

- Pipes A, B and C working together:

- A can fill in 12 hours, so in 1 hour it fills 1/12 of the tank.

- B fills in 16 hours, filling 1/16 of the tank in 1 hour.

- C empties in 24 hours, so in 1 hour it empties 1/24 of the tank.

- Combined rate for the first 4 hours:

- Total is (1/12 + 1/16 - 1/24) per hour.

- Calculate LCM (48): A = 4/48, B = 3/48, C = -2/48.

- Combined rate: (4 + 3 - 2)/48 = 5/48.

- In 4 hours, (5/48) * 4 = 20/48 = 5/12 of the tank filled.

- After 4 hours (A is closed):

- B fills with C: (1/16 - 1/24).

- LCM: 48; B = 3/48, C = -2/48.

- Combined rate: (3 - 2)/48 = 1/48.

- Remaining tank: 1 - 5/12 = 7/12.

- Time to fill the rest:

- Remaining (7/12) / (1/48) = 28 hours.

- Total time:

- 4 hours + 28 hours = 32 hours.

- Correct Option: Option 4 - 32 hours.

Submit Error