Given:
R and S together can complete a work in 60 days.
S and T together can complete the same work in 90 days.
R, S, and T all together can complete the work in 45 days.
Formula Used:
Work rate formula: Work done per day = 1 / Number of days
Calculation:
Let the total work be represented by W.
Work done per day by R and S together = 1 / 60
Work done per day by S and T together = 1 / 90
Work done per day by R, S, and T together = 1 / 45
Let work done per day by R, S, and T be R, S, and T respectively.
From the given information:
R + S = 1 / 60
S + T = 1 / 90
R + S + T = 1 / 45
Adding the first two equations:
⇒ (R + S) + (S + T) = 1 / 60 + 1 / 90
⇒ R + 2S + T = (90 + 60) / (60 × 90)
⇒ R + 2S + T = 150 / 5400
⇒ R + 2S + T = 1 / 36
Subtracting the third equation from the above equation:
⇒ (R + 2S + T) - (R + S + T) = 1 / 36 - 1 / 45
⇒ S = (45 - 36) / (36 × 45)
⇒ S = 9 / 1620
⇒ S = 1 / 180
Substituting S in R + S = 1 / 60:
⇒ R + 1 / 180 = 1 / 60
⇒ R = 1 / 60 - 1 / 180
⇒ R = (3 - 1) / 180
⇒ R = 2 / 180
⇒ R = 1 / 90
Substituting S in S + T = 1 / 90:
⇒ 1 / 180 + T = 1 / 90
⇒ T = 1 / 90 - 1 / 180
⇒ T = (2 - 1) / 180
⇒ T = 1 / 180
Therefore, work done per day by R and T together:
⇒ R + T = 1 / 90 + 1 / 180
⇒ R + T = (2 + 1) / 180
⇒ R + T = 3 / 180
⇒ R + T = 1 / 60
Thus, R and T together will take:
⇒ 1 / (1 / 60) = 60 days
The correct answer is option 4.