Deepak and Deepti with each other can complete a work in

Solution

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.