Question

A tank can be filled by tap P in 6 hours, Q in 8 hours and tap R can empty the full tank in 12 hours. If all three taps are opened simultaneously, how long will it take to fill the tank completely?
1. 25/6 hours
2. 24/5 hours
3. 15/6 hours
4. 20/3 hours

Answer 1

Correct Answer - Option 2 : 24/5 hours

Given:

Tap P filled = 6 hours

Tap Q filled = 8 hours

Tap R empty = 12 hours

Concept used:

Total capacity = LCM

The efficiency of inlet tap always positive and efficiency of outlet tap is always negative

Formula used:

Efficiency = Total capacity/Time

Calculation

Total capacity = LCM of 6, 8, 12 = 24

Tap	Time	Total capacity	Efficiency
P	6 hours	24	24/6 = 4
Q	8 hours	24	24/8 = 3
R	12 hours	24	24/12 = -2

 

Total efficiency of P, Q, and R = 4 + 3 – 2 = 5

Total time taken by P, Q, and R to fill the tank = (24/5) hours

∴ Total time taken by P, Q, and R to fill the tank is (24/5) hours