Ravi completes 1∕4 work in 15 days ⇒ Total time =15×4=60 days Chavi completes 1∕3 work in 18 days ⇒ Total time =18×3=54 days Dhani completes 1∕2 work in 24 days ⇒ Total time =24×2=48 days Work rate of each person: Ravi's rate =1∕60 work/day Chavi's rate =1∕54 work ∕ day Dhani's rate =1∕48 work ∕ day Combined rate of all three: Combined rate =1∕60+1∕54+1∕48 LCM of 60,54, and 48=2160 1∕60=36∕2160 1∕54=40∕2160 1∕48=45∕2160 Combined rate =(36+40+45)∕2160=121∕2160 work ∕ day Time to complete 3∕4 of the work: Time =(3∕4)÷(121∕2160) ⇒(3∕4)×(2160∕121) =1620∕121 Final Answer: 13