Aman and Rajan are working at a construction site. In some engineering experiment, Aman is constructing a wall, while Rajan is demolishing that wall. Aman can completely build the wall in 15 days, while Rajan will take 20 days to completely demolish the wall. In how many days will the complete wall be built for the first time if they work on alternate days, with Aman working on the 1
st
day?

Let the total work (capacity of the wall) be the LCM of 15 and 20, which is 60 units.
Efficiency of Aman (building) =
15
60
​
=+4 units/day

Efficiency of Rajan (demolishing) =
20
60
​
=−3 units/day

Since they work on alternate days starting with Aman:

Day 1 (Aman): +4 units

Day 2 (Rajan): −3 units

In 2 days, the net work done =4−3=1 unit.

To avoid overshooting the target when Aman finishes the wall on his turn, we subtract Aman's daily work from the total work:

Remaining target=60−4=56 units
Since 1 unit of work is completed in every 2-day cycle:
To complete 56 units of work, the number of days required =56×2=112 days.

At the end of 112 days, 56 units of the wall are complete.
On the 113
st
day, it is Aman's turn. He builds 4 units.

Total work completed=56+4=60 units
Thus, the wall is completed for the first time on the 113
st
day.