Deepak and Deepti with each other can complete a work in 60 days, Deepti and Danny in 90 days  and Deepak and Danny in 90 days. In how many days can Deepak, Deepti and Danny can complete the work if they work individually alone?

ATQ, We can say that let no of days taken by Deepak, Deepti and Danny when they work alone be taken as - x, y and z days individually. (1/x) + (1/y) = (1/60)..........eq(1) (1/y) + (1/z) = (1/90)...........eq(2) (1/x) + (1/z) = (1/90)............eq(3) While adding eq(1),(2) and (3) we get (2/x) + (2/y) + (2/z) = (1/60) + (1/90) + (1/90) = 2((1/x) + (1/y) + (1/z)) (3 + 2 + 2)/180 = (1/x) + (1/y) + (1/z) = (7/360)......eq(4) Now Subtract eq(4) with - eq 1, eq 2 and eq 3. eq(4) - (1) = (1/z) = (7/360) - (1/60) = (1/360) eq(4) - (2) = (1/x) = (7/360) - (1/90) = (1/120) eq(4) - (3) = (1/y) = (7/360) - (1/90) = (1/120) Therefore, no of days taken by Deepak, Deepti and Danny are 120,120 and 360 days individually.