Question

Two pipe A and pipe B can fill the tank in 12 hours and 16 hours respectively, while pipe C can empty the tank in 8 hours. If they all open together, then total time taken to fill the tank is:
1. 36 hours
2. 26 hours
3. 48 hours
4. 18 hours

Answer 1

Correct Answer - Option 3 : 48 hours

Given:

Time taken to fill tank by A = 12 hours

Time taken to fill tank by B = 16 hours

Time taken to empty tank by C = 8 hours

Concept used:

Total time = (Total volume)/(volume filled/empty in 1 hr)

Calculation:

Volume filled by A in 1 hr = 1/12 

Volume filled by B in 1 hr = 1/16 

Volume emptied by C in 1 hr = 1/8

Total volume filled after all pipes are open for 1 hr = 1/12 + 1/16 - 1/8                           [The efficiency of outlet pipe is opposite to inlet pipe] 

⇒ Required volume in 1 hr = (4 + 3 - 6)/48

⇒ Required volume filled in 1 hr = 1/48

Total time to fill tank = (Total volume)/(Volume filled in 1 hr)

⇒ Total time = 1/(1/48)

⇒ Total time = 48 hours

∴ The Total time taken to fill the tank is 48 hours.