Two persons A and B together can do a work in 10 days the same work can be
finished in 18 days if A works alone for 12 days and B works alone for 6 days, then
1) The time required for A to finish the work if he work alone is 15 days
2) The time required for B to finish the work if he work alone is 30 days
3) The time required for A to finish the work if he work alone is 20 days
4) The time required for B to finish the work if he work alone is 40 days
Let a be number of days it takes for person A to finish the work alone.
Let b be number of days it takes for person B to finish the work alone.
Let 1 represent 100% of the job.
We know that 10/a + 10/b = 1. (1)
We also know that 12/a + 6/b = 1. (2)
(1): Multiplying both sides by ab, we have: 10b + 10a = ab (3)
(2): Multiplying both sides by ab, we have: 12b + 6a = ab (4)
(3) = (4): 10b + 10a = 12b + 6a
Dividing both sides by 2, we have: 5b + 5a = 6b + 3a.
Moving and combining like terms to one side, we have b = 2a (5).
Substituting (5) into (1): 10/a + 10/2a = 1.
Multiplying both sides by a we have 10 + 5 = a.
So a=15.
Thus b = 30.
Person A will take 15 days, person B will take 30 days.
