If 6 engineers can complete a work in 5 days and 5 skilled workers can complete the same work in 7 days, then the time taken (in days) to complete the same work by 7 engineers and 4 skilled workers will be:

Correct option is C

Given:
6 engineers can complete a work in 5 days
5 skilled workers can complete the same work in 7 days
Solution:
Time taken by 7 engineers to complete the work =  $$\frac{(6 ×5)}{7} = \frac{30}{7}$$​​
Time taken by 4 workers to complete the work= $$\frac{(5 ×7)}{4} = \frac{35}{4}$$​

Time taken by both engineers and worker working together:
​$$\frac{1}{(\frac{7}{30}+\frac{4}{35})} \\\ \\\frac{1}{(\frac{(49+24)}{210})} \\\ \\=\frac{210}{73}= 2 \frac{64}{73}$$​​