Ravika alone can complete three-fifth of a work in 105 days. Mallika can complete one-third of work in 50 days. In how many days Ravika and Mallika working together, can complete $$\frac{26}{35}$$ of the work?

Ravika can alone complete three-fifth of work in 105 days.

Time taken by Ravika to complete the work = $$\frac{5}{3}\times{105}$$ = 175

Similarly, Time taken by Mallika to complete the work = $$\frac{3}{1}\times{50}$$ = 150

Taking LCM of (175,150) we get 1050.

Hence the work capacity of Ravika =$$\frac{1050}{175}$$= 6

The work capacity of Mallika =$$\frac{1050}{150}$$ =7

The total work capacity of Ravika and Mallika = 7 + 6 =13.

So the total time taken for completing $$\frac{26}{35}$$ of work = $$\frac{26}{35}\times\frac{1050}{13}$$= 60 days.