Question

Pipes P and Q can fill a tank in 12 hours and 16 hours respectively, and R can empty it in 8 hours. If all three are opened at 8:00 am, at what time will one-fourth of the tank be filled? 
1. 1:00 pm
2. 3:00 pm
3. 8:00 pm
4. 10:00 pm

Answer 1

Correct Answer - Option 3 : 8:00 pm

Given: 

P and Q can fill a tank in 12 hours and 16 hours respectively, R can empty in 8  hours.

Calculation: 

Take capacity of tank is LCM of (12, 16, and 8) = 48 unit

P fill in one hour = 48/12 = 4 unit

Q fill in one hour = 48/16 = 3 unit

R empty in one hour = 48/8 = 6 unit

Now, 

All work together then fill in one hour = 4 + 3 - 6 = 1 unit

 Then, Time taken to fill 1/4th of tank by P, Q and R together 

⇒ (48 × 1/4) ÷ 1

⇒ 12 hour

∴ The 1/4th part of tank filled at 8:00 pm.