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 ?
Answer & explanation
Correct answer: option 2
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