Two workers R and S working together completed a work in 7 days. If R worked thrice as efficiently as he actually did and S worked \(\frac{1}{5}\) as efficiently as he actually did, the work would have been completed in 5 days. R would require how many days to complete the work ?

\(\frac{49}{3}\)  days

Total work = Efficiency  × Number of days 

Let efficiency of R = R unit   , efficiency of S = S unit 

according to question ,

 R and S working together completed a work in 7 days

Total work  =  (R + S) × 7   --------- ( 1 ) 

 If R worked thrice as efficiently as he actually did and S worked \(\frac{1}{5}\) as efficiently as he actually did, the work would have been completed in 5 days. 

Total work  =  (3R + \(\frac{S}{5}\)) × 5   ------ ( 2 ) 

put equation 1 equals to equation 2

 (R + S) × 7 = (3R + \(\frac{S}{5}\)) × 5

 7R + 7S = 15R + S

 8R = 6S  

 so ratio of        R  :  S

                        3  :  4

Total work = (3 + 4) × 7 = 49 unit

R would require = \(\frac{49}{3}\) = 16\(\frac{1}{3}\) days to complete the work