R and S together can complete a work in 60 days. S and T together can complete the same work in 90 days. If R, S, and T work together, the same work is completed in 45 days. How many days will R and T together take to complete the same work?
Show answer & explanation
Correct answer: D
Explanation
The correct answer is Option 4 i.e. 60 days.
R and S together can complete a work in 60 days. S and T together can complete the same work in 90 days. If R, S, and T work together, the same work is completed in 45 days
L.C.M(60, 45 and 90) = 360
The efficiency of R and S = 360/60 = 6 units
The efficiency of S and T = 360/90 = 4 units
The efficiency of R, S, and T = 36/45 = 8 units
So,
The efficiency of R = 8 - 4 = 4 units
The efficiency of T = 8 - 6 = 2 units
Thus,
Time taken by R and T = 360/(4 + 2) = 360/6 = 60 days