Two pipes A and B can fill a cistern in 36 minutes and 48 minutes, respectively. Both the pipes are opened at the same time and pipe B is closed after some time. If the cistern gets filled in half an hour, then after how many minutes was pipe B closed?

Correct option is A

Given:

A fill a cistern in 36 minutes

B fill a cistern in 48 minutes

Cistern is filled in 30 minutes

Formula Used:

Efficiency × Time taken = Total capacity of tank

Total capacity of cistern = LCM of time taken

Solution:

Total capacity of cistern = LCM of 36 and 48

Total capacity of cistern = 144 units

Efficiency by A to fill cistern = $$\frac{144}{36}$$​= 4

Efficiency by B to fill cistern = $$\frac{144}{48}$$​ = 3

Pipe B is closed after some time, but pipe A worked for 30 minutes,

In 30 minutes,

Cistern filled by pipe A = 30 × 4 = 120

Remaining units to be filled,

144 – 120 = 24

Remaining 24 units was filled by pipe B,

Time taken by pipe B,

= $$\frac{24}{3}$$​ = 8 minutes.

Pipe B closed after 8 minutes.