Type 1 workers are two-and-a-half times as efficient as Type 2 workers. If 12 Type 1 workers can complete a task in 10 days, how many days would it take 6 Type 1 and 10 Type 2 workers to complete the same task?

12 Type1 workers completed = 10 days

1 Type1 worker will complete$$=12\times10= 120 days$$

Since Type1 worker 2.5 times efficient than Type2

1 type2 worker complete $$=2.5\times120=300 days$$

Total unit of work $$=L.C.M of (120 and 300)=600$$

1 Type1 worker unit of work in one day $$\frac{600}{120} =5$$

1 Type2 worker unit of work in one day $$\frac{600}{300} =2$$

Now, 6 Type1 workers job unit + 10 Type2 workers work unit in one day $$=6\times5+10\times2 =30+20= 50$$

total time to complete work $$=\frac{600}{50} =12 $$days