Stuart, Jack and Leo are colleagues working in a plant. Stuart and Jack can do a work in 10 days, Jack and Leo can do the same work in 15 days while Stuart and Leo can do it in 12 days. All of them started the work together. After two days, Leo was shifted to some other work. How many days will Stuart and Jack take to finish the rest of the work?

Let the total work be 120 units.

Let efficiencies of Stuart = s , Jack = j , Leo = l.

We know, Efficiency x Time = Work done.

Forming 3 eqns.:

s + j = 120 units/ 10 days = 12 units/day

j + l = 120 units/ 15 days = 8 units/day

s + l = 120 units/ 10 days = 10 units/day

On solving the above 3 eqns. , we get

s = 7 units/day , l = 3 units/day , j = 5 units/day

All 3 start together but Leo leaves after 2 days.

(15 x 2) + (12 x n) = 120

=> n = 7.5 days

$$\therefore\ $$ To finish rest of the work, Stuart and Jack take 7.5 days.