X can complete 5/7 part of a work in 10 days and Y can complete 3/4 part of the same work in 9 days. In how many days will both complete 13/21 part of the total work?

Let total work to be done = 1 unit

X complete $$\frac{5}{7}^{th}$$ work in 10 days, => X's efficiency = $$\frac{5}{7\times10}=\frac{1}{14}$$ units/day

Similarly, Y's efficiency = $$\frac{3}{4\times9}=\frac{1}{12}$$ units/day

Thus, (X+Y)'s 1 day's work = $$\frac{1}{14}+\frac{1}{12}=\frac{13}{84}$$ units/day

Now, 13/21 part of total work = $$\frac{13}{21}$$ units

=> Time taken = $$(\frac{13}{21})\div(\frac{13}{84})$$

= $$\frac{13}{21}\times\frac{84}{13}=4$$ days

=> Ans - (B)