Two inlet pipes A and B can fill a cistern in 30 minutes and 36 minutes, respectively. Initially, only A is opened for 10 minutes. After 10 minutes, A is closed and B is opened. In how much time (in minutes) will the inlet pipe B fill the remaining part of the cistern?

Correct option is C

Given:

Pipe A fills the cistern in 30 minutes

Pipe B fills the cistern in 36 minutes

Pipe A is opened for 10 minutes, then closed

Pipe B is opened to fill the remaining part

Solution:

Rate of A = $$\frac{1}{30}$$​​

Rate of B = $$\frac{1}{36}$$​​

Work done by A in 10 min = $$\frac{10}{30} = \frac{1}{3}$$​​

Remaining work = $$1 - \frac{1}{3} = \frac{2}{3}$$​​

Time taken by B = $$\frac{2/3}{1/36}$$​​

​$$= \frac{2}{3} \times 36$$​​

= 24 minutes

Alternate Solution:

total work = LCM of 30 and 36 = 180 units 

Efficiency of A = $$\frac{180}{30}$$​ = 6 units/min

Efficiency of B = $$\frac{180}{36}$$​ = 5 units/min

Work done by A in 10 minutes = 6 × 10 = 60 units

Remaining work = 180 - 60 = 120 units

Time for B to do 120 units = $$\frac{120}{5}$$​ = 24 minutes