Two pipes can fill a cistern separately in 40 minutes and 60 minutes, respectively. They can together fill the cistern in:

Correct option is A

Given:

Pipe 1 can fill the cistern in 40 minutes.

Pipe 2 can fill the cistern in 60 minutes.

Concept Used:
The rate at which a pipe fills the cistern is the reciprocal of the time taken. 

Solution:

Rate of Pipe 1 $$= \frac{1}{40}$$​ cisterns per minute.

Rate of Pipe 2 =$$\frac{1}{60}$$​ cisterns per minute.
Combined rate of both pipes:

Combined rate =$$\frac{1}{40} + \frac{1}{60}$$​

​$$= \frac{3}{120} + \frac{2}{120} = \frac{5}{120} = \frac{1}{24}$$​

So, the combined rate of both pipes is $$\frac{1}{24}$$​ cisterns per minute.

Therefore, they can together fill the cistern in 24 minutes.

Alternate Method:

Work = 1 unit (LCM method)

LCM of 40 and 60 = 120 units (Assume total work = 120 units)

Pipe A's 1-minute work = 120 ÷ 40 = 3 units

Pipe B's 1-minute work = 120 ÷ 60 = 2 units

Together, 1-minute work = 3 + 2 = 5 units

Time to fill cistern = 120 ÷ 5 = 24 minutes

Thus, both pipes together can fill the cistern in 24 minutes.

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