X can complete a task in 15 days, and Y can complete the same task in 20 days. If X and Y work on alternate days starting with X, in how many days will the work be completed?

Correct option is A

Given:
X can do 60 units in 15 days
Y can do 60 units in 20 days 
Formula Used:
$$\text{Efficiency} = \frac{\text{Total Work}}{\text{Total Time Taken}}$$​​
Solution:
Total work = LCM of 15 and 20 = 60 units
X can do 60 units in 15 days
→ X's 1-day work = 60 ÷ 15 = 4 units/day
Y can do 60 units in 20 days
→ Y's 1-day work = 60 ÷ 20 = 3 units/day
Work done in 2 days (X + Y working alternate days) = 4 + 3 = 7 units
In 16 days (8 cycles), total work = 7 ×8  = 56 units
Work done in 16 days = 56 units
 Remaining work = 60 – 56  = 4 units
Now, 4 unit remaining work will be completed by X on 17th day. 
Total time to complete whole work = 16+ 1= 17 days