Sarasai019 wrote:
John can build a wall in 30 days and Peter can demolish the same wall in 40 days.If they work on alternate days with John starting the job on the 1st day , then in how many days will the wall be built for the first time?
I get 240 as the answer. But certain people say its 233. Not sure about the right answer to this. Any help solving this is appreciated! Thanks
John can build a wall in 30 days and Peter can demolish the same wall in 40 daysSo, in ONE day, John can build 1/30 of the entire wall
And, in ONE day, Peter can demolish 1/40 of the entire wall
So, AFTER TWO DAYS, the portion of the wall standing = 1/30 - 1/40 = 1/120
So, AFTER TWO DAYS, 1/120 of the wall is built (and remains standing)
So, after FOUR DAYS, 2/120 of the wall is built (and remains standing)
And after SIX DAYS, 3/120 of the wall is built (and remains standing)
.
.
.
And after 232 DAYS, 116/120 of the wall is built (and remains standing)
On DAY 233, it's John's turn to build.
Remember that, in ONE day, John can build 1/30 of the entire wall
In other words, in ONE day, John can build 4/120 of the entire wall
So, after 232 DAYS, 116/120 of the wall was built, and on the 233rd day, John built the remaining 4/120 of the wall.
So, WALL COMPLETE!!
Answer: 233
Cheers,
Brent