The work efficiency of Mahendra, Viraj, and Ronit is 1 ∶ 2 ∶ 4 and they can finish the work in 40 days. Find the time taken by Viraj and Ronit to do the work together.
Given: The work efficiency of Mahendra, Viraj and Ronit is 1 ∶ 2 ∶ 4 Concept Used: Time ∝ 1/Efficiencey If a person can complete a work in t days then in 1 day he will do 1/t part of the work. Calculation: Ratio of work efficiency of Mahendra, Viraj and Ronit is 1 ∶ 2 ∶ 4 ⇒ Ratio of time taken by Mahendra, Viraj and Ronit to complete the work is 1 : 1/2 : 1/4 ⇒ 4 : 2 : 1 Let the time taken by Mahendar, Viraj and Ronit be 4x, 2x and x days respectively Together they can finish the work in 40 days ⇒ (1/4x) + (1/2x) + (1/x) = 1/40 ⇒ 7/4x = 1/40 ⇒ x = 70 ∴ Viraj can complete the work in = 2x = 2 × 70 = 140 days Ronit can complete the work in = x = 1 × 70 = 70 days Together they can finish the work ⇒ (1/140) + (1/70) = 6/280 = 3/140 ∴ Time taken by Viraj and Ronit to do the work together is 140/3 days