Question

There are 3 pipes A, B and C that are attached to an empty cistern. Pipe A and pipe B can fill the cistern in 4.8 hours and 6.4 hours respectively and pipe C can drain the filled cistern in 9.6 hours. Find the total time taken to fill 5/24th of the total volume of the tank, if all the pipes work simultaneously. 
1. 0.8 hours 
2. 1 hour
3. 2 hours 
4. 4 hours 

Answer 1

Correct Answer - Option 1 : 0.8 hours 

Given : 

There are 3 pipes A, B and C that are attached to an empty cistern. Pipe A and pipe B can fill the cistern in 4.8 hours and 6.4 hours respectively and pipe C can drain the filled cistern in 9.6 hours.

Calculations :

Let the total time be 't' to fill the whole cistern

Pipe A per hour work = (1/4.8) units

Pipe B per hour work = (1/6.4) units 

Pipe C per hour work = (1/9.6) units 

So, 

⇒ (1/4.8) + (1/6.4) - (1/9.6) = 1/t    (pipe C is drain pipe so taken with -ve sign)

⇒ 1/t = 50/192 

⇒ t = 192/50 

Time taken to fill 5/24th volume of the tank = (5/24) × (192/50) 

⇒ 8/10 = 0.8 hour

∴ Option 1 will be the correct answer.