P can do as much work in 6 days as Q can do in 7, and Q can do as much work in 8 days as R in 5 days. In what time will R do a piece of work which P can do in 8 days ?

5\(\frac{5}{6}\) days

According To Question ,

       P × 6 = Q × 7        &     Q ×8 = R × 5   ( Total work = Efficiency  × Number of days  ) 

Ratio of efficiency       P    :   Q                &       Q    :     R

                                 7    :   6                          5    :     8  

So                                         P     :     Q     :     R

                                         7× 5    :   6 × 5      

                                                        5 × 6   :    8 × 6

 Combined ratio                      35    :     30    :     48

Total work = Efficiency  × Number of days 

let R completed same work in d days as done by P in 8 days 

P × 8 days work = R × d days work

35 × 8 = 48 × d

 d = \(\frac{35}{6}\) = 5\(\frac{5}{6}\) days