Hondo and Rana can do a piece of work in 25 days. Rana & Chatur together can do it in 35 days. If Hondo is thrice as good a workman as Chatur, find in how many days Rana alone can do the work?

43\(\frac{3}{4}\) days

Hondo     :     Chatur

       3     :      1

Make total work equal

(Hondo + Rana) × 25 = (Rana + Chatur) × 35

5 Hondo + 5 Rana = 7 Rana + 7 Chatur

5 Hondo - 7 Chatur = 2 Rana

5 × 3 - 7 × 1 = 2 Rana

           Rana = 4

Total work = (3 + 4) × 25 = 175

Time taken by Rana = \(\frac{175}{4}\) = 43\(\frac{3}{4}\) days