A can do a piece of work in 7 days of 9 hours each, whereas B can do same work in 6 days of 7 hours each. How long will they take to do the work together working $$4\frac{1}{5}$$ hours a day? 

Correct option is D

Given:

A can do work in 7 days of 9 hours each

B can do same work in 6 days of 7 hours each

They work for $$4\frac{1}{5}$$​ hours a day

Formula Used:

Work done = Efficiency of each worker$$\times$$​ Time

Solution:

A can complete the work in  = $$7 \times 9$$ = 63 hours

A’s 1 hour’s work = $$\frac{1}{63}$$​​

B can complete the work in = $$6 \times 7 = 42 \ hours$$​​

B’s 1 hour’s work = $$\frac{1}{42}$$​​

(A+B)’s 1 hour’s work =$$\frac{1}{63} +\frac{1}{42}$$​​

​$$= \frac{2+3}{126}$$​​

$$= \frac{5}{126}$$​

Both will finish the work in $$\frac{126}{5}$$​hours

Number of days required to finish working  $$4\frac{1}{5}$$ hours a day =$$\frac{21}{5}$$hours each = $$\frac{126}{5} hours \div \frac{21}{5} = 6 days$$​​

They will take 6 days to complete the work.