A can do a piece of work in 15 days and B can do the same work in 20 days. The time taken by them working together to do the same work is:

Correct option is B

Given:

A can do a piece of work in 15days

B can do a piece of work in 20days

Formula Used:

Let total work to fill the tank be 1.

Then work done by a pipe in 1 hour = $$\frac{1}{\text{Total time to fill}}$$​​

Solution:

Work done  by A in one day =  $$\frac{Total\ Work}{Total\ time\ } =\frac{1}{15}$$​​

Work done  by B in one day =  $$\frac{Total\ Work}{Total\ time\ } =\frac{1}{20}$$​​

Work done by A and B in one day working together = $$\frac{1}{15} + \frac{1}{20} =\frac{4+3}{60} =\frac{7}{60}$$​​

Time taken to complete the work by A and B working together = $$\frac{1}{\frac{7}{60}} =\frac{60}{7}days = 8\frac{4}{7}days$$​​

Alternative Method:

Total Work = Efficiency × Time

LCM of 15 and 20 = 60

Efficiency of  A  = $$\frac{60}{15}= 4units$$​​

Efficiency of B $$=\frac{60}{20}$$​ =3 units

Total efficiency of A and B = 4 + 3 = 7 units

Total time taken to complete the work =$$\frac{60}{7} =8\frac{4}{7}days$$​​