A tank has two inlets, A and B, which can fill it in 15 hours and 20 hours, respectively. An outlet C can empty the full tank in 12 hours. If A, B and C are opened together when the tank is empty, then in how much time will the tank be filled?

Correct option is B

Given:

Inlet A can fill the tank in 15 hours 

Inlet B can fill the tank in 20 hours

Outlet C can empty the tank in 12 hours 

Solution:

Rate of A = $$\frac 1{15}$$ of the tank per hour

Rate of B = $$\frac 1{20}$$ of the tank per hour

Rate of C = $$\frac{−1}{12}$$​of the tank per hour (negative because it is emptying the tank)

The combined rate of A, B, and C is:

Combined rate =$$\frac{1}{15} + \frac{1}{20} - \frac{1}{12}$$​

= $$\frac{4}{60} + \frac{3}{60} - \frac{5}{60} = \frac{4 + 3 - 5}{60} = \frac{2}{60} = \frac{1}{30}$$​

Since the combined rate of A, B, and C is $$\frac1{30}$$​, the time taken to fill the tank is the reciprocal of the rate:

Time to fill the tank $$= \frac{1}{\frac{1}{30}} = 30 \text{ hours}$$​

The tank will be filled in 30 hours.

Alternate Method:

Time to fill the tank = $$\frac{60}{4+3-5}=\frac{60}2$$ = 30 hours