Two pipes can fill a tank in 30 hours and 40 hours, respectively. Find the time (in hours) taken to fill the tank when both the pipes are opened simultaneously.

Correct option is A

Given:

Time taken by Pipe A = 30 hours

Time taken by Pipe B = 40 hours

Formula Used:

Combined Rate = $$\frac{1}{\text{Combined Rate}}$$​​

Solution:

Combined work rate of A + B = $$\frac{1}{30} + \frac{1}{40}$$​​

​$$= \frac{4 + 3}{120} = \frac{7}{120}$$​​

Time = $$\frac{1}{\frac{7}{120}} = \frac{120}{7} = 17\frac{1}{7}\, \text{hours}$$​ 

Alternate Solution: 

Total Work = LCM(30, 40) = 120 unit 

Efficiency of A = $$\frac{120}{30}$$ = 4

​Efficiency of B = $$\frac{120}{40}$$​ = 3 

Time to fill together = $$\frac{120}{4+3} = 17\frac{1}{7}\, \text{hours}$$​​