Three water pipes m, n and p, take 5, 6 and 12 hours, respectively, to fill a water tank. If all three pipes are opened at the same time, then the required time to fill the water tank will be:

Correct option is D

Given:

Pipe m fills in 5 hours 

Pipe n fills in 6 hours 

Pipe p fills in 12 hours 

Solution:

Combined rate = $$\frac{1}{5} + \frac{1}{6} + \frac{1}{12}$$​​

​$$= \frac{12 + 10 + 5}{60}$$​​

​$$= \frac{27}{60} = \frac{9}{20} \text{ tank/hour}$$​​

Time to fill 1 tank = $$\frac{20}{9} \text{ hours} = 2\frac{2}{9} \text{ hours}$$​​

Alternate Solution:

LCM of 5, 6, 12 = 60 litres (capacity of tank)

Rates:

m: $$\frac{60}{5}$$​ = 12 L/hour

n: $$\frac{60}{6}$$​ = 10 L/hour

p: $$\frac{60}{12}$$​ = 5 L/hour

Combined rate = 12 + 10 + 5 = 27 L/hour

Time to fill 60 L = $$\frac{60}{27} = \frac{20}{9} \text{ hours} = 2\frac{2}{9} \text{ hours}$$​​