A can build a wall in 10 days, working alone, B can build the same wal

A’s building rate is 1/10 per day, B’s building rate is 1/20 per day and C’s demolishing rate is 1/8 per day. So for the first 3 days, 1/10 + 1/20 - 1/8 = 4/40 + 2/20 - 5/40 = 1/40 of the wall is built.

So one might think it will take 3 x 40 = 120 to complete the wall since it takes 3 days to build 1/40 of the wall. However, this is not right, since once the whole wall is built for the first time (on certain day by either A or B), we don’t care whether C will break it or not. So let’s look the answer choices. The first answer choice is 102. So let’s see what happen in 102 days.

In 102 days, 34/40 of the wall is built since 102/3 = 34.

Then the next day (103rd day), 34/40 + 1/10 = 34/40 + 4/40 = 38/40 of the wall is built and the following day (104th day), 38/40 + 1/20 = 38/40 + 2/20 = 40/40 = 1 complete wall is built.

Answer: 2

Rate of work of 3 days = 1/10 + 1/20 - 1/8 = 1/40th of the wall

Now the wall will be complete the first time when A and B complete it but C doesn't get a chance to break it. So when 1/10 + 1/20 = 3/20th (= 6/40th) of the wall is leftover for the first time.
So 34/40th of the wall should be completed.
Since 1/40th of the wall is made in 3 days, 34/40th will be made in 3*34 = 102 days

Then A and B will work on it for 2 days to complete the rest of 6/40th of the wall. So total days taken = 104 days

Answer (B)

rate of A = 1/10
rate of B = 1/20
together = 3/20
and C rate = -1/8
all together they can work 3 days = 3/20-1/8 ; 1/40
so in terms of total work being done A& B are completing 6/40 of the wall in two days; left with 34/40 of the work which can be completed in
34*3 = 102 days ; also 2 days of 6/40 to be added to 102 days to complete wall
IMO B 104 days

In one day, A builds 1/10 of the wall, B builds 1/20 of the wall, and C breaks 1/8 of the wall. When A, B and C work on consecutive days,

1/10 + 1/20 - 1/8 = 4/40 + 2/40 - 5/40 = 1/40

of the wall gets build. However, we need to find the number of days till the wall is built for the first time; therefore, we need to find the number of terms in the sum 1/10 + 1/20 - 1/8 + 1/10 + 1/20 - 1/8 + 1/10 + … when the sum becomes greater than or equal to 1 for the first time. The sum will become greater than or equal to 1 after the addition of either of the terms 1/10 or 1/20; therefore, let’s group this summation as:

1/10 + 1/20 + (-1/8 + 1/10 + 1/20) + (-1/8 + 1/10 + 1/20) + …

As we previously calculated, the sum of the terms in the parentheses is 1/40. The sum of the first two terms is 1/10 + 1/20 = 4/40 + 2/40 = 6/40. Thus, after those first two days, we have 1 - 6/40 = 34/40 of the job remaining. As 1/40 of the job gets done in successive days of work by C, A, and B (in that order), we need this cycle to repeat 34 times, or 34 * 3 = 102 days. Adding the work done in the first two days by A and B, we find that the wall gets built for the first time in 102 + 2 = 104 days.

Answer: 2/ B

I would prefer to do these kinda questions using LCM method, but someone already posted that one. So, i gonna post different approach.
Efficiency of A= 100/10=10
Efficiency of B= 100/20=5
Efficiency of C=(-)100/8=-12.5
Their combined efficiency in every 3-days cycle=10+5-12.5=2.5
Number of days required for doing 85% of work=(85/2.5)*3=102
By 103rd day, work finished=85+10=95%
and by 104th day, wor finished= 95+5=100%
hence 104 is the required answer.

Given:
1. A can build a wall in 10 days, working alone, B can build the same wall in 20 days, working alone and C can break the entire built wall in 8 days, working alone.
2. The three of them work alone on the wall on successive days with A working on first day, B on second day and C on third day and the cycle then repeats.

Asked: In how many days will the wall be built for the first time?

A's work done in 1 day = 1/10
B's work done in 1 day = 1/20
C's work done in 1 day = -1/8

A, B & C's work done in 3 days = 1/10 + 1/20 -1/8 = 3/20 - 1/8 = (6-5)/40 = 1/40
A, B & C's work done in 1 day = 1/120

A, B & C's work done in 34*3 days = 36/40
Work balance = 6/40 = 3/20

Which can be done by A & B in 2 days

Total time taken to build the wall = 34*3 + 2 = 102+2 = 104 days

IMO B

A can build a wall in 10 days, working alone, B can build the same wall in 20 days, working alone and C can break the entire built wall in 8 days, working alone. The three of them work alone on the wall on successive days with A working on first day, B on second day and C on third day and the cycle then repeats. In how many days will the wall be built for the first time?

I don't know how many of you prefer the LCM method over the fraction method to solve time and Work-related questions. For me, Since we are using integers in the LCM method, it is more easy to connect and understand the question.

Let's apply the LCM method here as well,

Assume the work as LCM ( 10,20,8 ) = 40 units

Now, let's calculate their per day work, Per day Work = Total Work done/Time taken

Per day work of A is 40/10 = 4 units/day

Per day work of B is 40/20 = 2 units/day

Per day work of A is 40/8 = -5 units/day. * We put negative sign as its a negative work

The three of them work alone on the wall on successive days with A working on the first day, B on the second day, and C on the third day, and the cycle then repeats.
Total work completed by them in 3 days (A working on the first day, B on the second day, and C on the third day )= 4 + 2 - 5 = 1 unit in 3 days.

Since 40 units of work is to be completed, then Time taken would be 40 * 3 = 120 days i.e Option D.

If you got Option D as the answer that means you have fallen for the GMAT trap. Most of the students would have fallen for it. This is evident from the question statistics i.e 59% made it wrong.

Since C's job is to destroy the wall and he's working on the third day, there could be a chance that the wall will be completed a day before C's turn during the last stretch. This thought process should lead you to do the detailed analysis of work done by them in the last 3 days.

Since A and B can do 6 units in 2 days, let us calculate the time taken to complete 34 units i.e 40 units - 6 units.

Why 34 units? because we know that if we calculate the time for 34 units, A and B can complete the remaining work of 6 units in the next 2 days without C's intervention on the third day.

34 units of work will be completed in 34 * 3 = 102 days.

The next day, A will be completing 4 units and the day after B will be completing 2 units. So a total of 6 units will be completed by A and B in the next 2 days.

So by the end of 104 days, total work of 40 units will be completed. C will not get a chance to destroy it as work is already completed.

Option B is the answer.

Thanks,
Clifin J Francis,
GMAT QUANT SME

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