Question

Pipes A and B can fill a tank in 20 hours and 30 hours respectively, whereas pipe C alone can empty the full tank in 10 hours. Pipes A and B are opened together for \(3\frac{1}{2}\) hours and then closed. If pipe C is opened, It will empty the tank in:
1. 2 hours 15 minutes
2. 2 hours
3. 2 hours 55 minutes
4. 2 hours 45 minutes

Answer 1

Correct Answer - Option 3 : 2 hours 55 minutes

Given:

Pipe A in 20 hours. 

Pipe B in 30 hours.

Pipe C empty in 10 hours.

Pipe A and B are opened for \(3\frac{1}{2}\)hours.

Formula Used:

Efficiency ×  Time taken = Total capacity of tank

Total capacity of tank = LCM of time taken

Calculation:

Total capacity of tank, 

⇒ LCM of 20, 30, and 10

⇒ 60

Total capacity of tank is 60 units.

Efficiency of Pipe A = 60/20

⇒ Efficiency of Pipe A = 3 units/hour.

Efficiency of Pipe B = 60/30

⇒ Efficiency of Pipe B = 2 units/hour.

Efficiency of Pipe C = 60/10

⇒ Efficiency of Pipe C = 6 units/ hour

Pipe A and B opened for \(3\frac{1}{2}\)hours.

⇒ Combine efficiency of A + B,

⇒  3 + 2   

⇒ 5 units/hour

\(3\frac{1}{2}\)hours = 7/2 hours

⇒ 5 × 7/2

⇒ 35/2 units filled  

Now Pipe C will work,

It will empty the 35/2 units in,

⇒ Time = (35/2)/6

⇒ Time = 35/12

⇒ Time = \(2\frac{{11}}{{12}}\)

⇒ Time = 2 hours and 55 minutes.

∴ Pipe C will empty the tank in 2 hours and 55 minutes.