A can complete a work in 16 days and B can complete the same work in 26 days. What will be the number of days required by A and B to complete the same work together?

Correct option is C

Given:

A can do work in 16 days

B can do the same work in 26 days

Formula Used:

Let total work be 1.

Then work done 1 day $$=\frac{1}{Total\ time\ to\ work}$$​​

Solution:

A’s one day’s work =$$\frac{1}{16}$$​​

B’s one day’s work =$$\frac{1}{26}$$​​

A and B’s one day work together = $$\frac{1}{16}+\frac{1}{26}$$​​

​$$= \frac{13+8}{208}=\frac{21}{208}$$​​

Time taken by by both A and B working together =$$\frac{1}{\frac{21}{208}} = \frac{208}{21} = 9\frac{19}{21}$$​​

Alternative Method:

Total Work = Efficiency $$\times$$​ Time

Total Work = LCM of 16 and 26  =208

Efficiency of A = $$\frac{208}{16}$$ = 13 units per day.

Efficiency of B = $$\frac{208}{26}$$= 8 units per day

Efficiency of both A and B = 13 + 8 = 21 units per day

Time taken by by both A and B working together = $$\frac{208}{21} = 9\frac{19}{21}$$​​