Suraj can complete a certain work in the same time in which Manoj and Rajesh together can complete it. If Rajesh can alone complete it in 28 days and Suraj and Manoj together can complete it in 14 days, then in how many days can Manoj alone complete it?

Explanation

Given: Suraj can complete a certain work in the same time in which Manoj and Rajesh together can complete it. Rajesh can alone complete it in 28 days and Suraj and Manoj together can complete it in 14 days Concept used: Total work = Efficiency of the workers × time taken by the workers Calculation: Let total work be 28 units [As LCM of 14, 28 is 28] So, efficiency of Rajesh = 28/28 = 1 unit/day Efficiency of Suraj and Manoj = 28/14 = 2 units/day According to the question, Efficiency of Suraj = Efficiency of Manoj + Rajesh ⇒ Suraj = Manoj + 1 ⇒ Suraj + Manoj = Manoj + 1 + Manoj ⇒ 2 = 2Manoj + 1 ⇒ 2 - 1 = 2Manoj ⇒ 1 = 2Manoj ⇒ Manoj = 0.5 So, efficiency of Manoj = 0.5 Required Time = 28/0.5 ⇒ 56 days. ∴ Manoj alone completes it in 56 days.