A tank has two inlets A and B that can fill it in 5 h and 6 h respectively. An outlet C can empty the full tank in 30 h. If all the three pipes are opened together in the empty tank, how much time will the pipes take to fill the tank?

Correct option is D

Given:

Inlet A fills the tank in 5 hours.

Inlet B fills the tank in 6 hours.

Outlet C empties the full tank in 30 hours.

Solution:

The rate of filling or emptying the tank is:

Rate of A =$$\frac{1}{5}$$​ (since A fills the tank in 5 hours)

Rate of B =$$\frac{1}{6}$$​ (since B fills the tank in 6 hours)

Rate of C =$$-\frac{1}{30}$$​(since C empties the tank in 30 hours)

Combined rate $$= \frac{1}{5} + \frac{1}{6} - \frac{1}{30}$$​

Combined rate =$$\frac{6}{30} + \frac{5}{30} - \frac{1}{30} = \frac{10}{30} = \frac{1}{3}$$​

This means that all three pipes together fill $$\frac{1}{3}$$​ of the tank per hour.

To fill the entire tank, the time required is the reciprocal of the combined rate:

Time taken $$= \frac{1}{\frac{1}{3}} = 3 \text{ hours}$$​

The pipes will take 3 hours to fill the tank.

Alternate Method:

Time taken =$$\frac{30}{11-1}=\frac{30}{10}=3$$ hours​