Problem Solving

50 persons can complete the work in 100 days. In how many days will the work be completed if 10 persons start the work and 10 person join after every 10 days?

Total amount of work is 50*100=5000 man-days

if x is the number of days to complete the work then

100+200+300+..till x terms =5000
or x/2{200+(x-1)100}=5000
or 100x+50x^2-50x=5000
or 50x^2+50x-5000=0
or x^2+x=100

for x=10, LHS becomes 10*11=110

hence the work will be complete on 100th day

gmatmachoman wrote:50 persons can complete the work in 100 days. In how many days will the work be completed if 10 persons start the work and 10 person join after every 10 days?

Total work = 5000 man days

Total work done in first 10 days = 100 man days
Total work done in second 10 days = 200 man days
Total work done in nth 10 days = n*100 mandays

sum = n(n+1)*50

now n(n+1)*50> 5000
n(n+1)> 100
n>10

till 10th 10 days work worth 4500 man days would be done

We have 110 people to finish remaining 500
who will finish it in 500/110 days
total days = 100 + 50/11

ajith wrote:

gmatmachoman wrote:50 persons can complete the work in 100 days. In how many days will the work be completed if 10 persons start the work and 10 person join after every 10 days?

Total work = 5000 man days

Total work done in first 10 days = 100 man days
Total work done in second 10 days = 200 man days
Total work done in nth 10 days = n*100 mandays

sum = n(n+1)*50

now n(n+1)*50> 5000
n(n+1)> 100
n>10

till 10th 10 days work worth 4500 man days would be done

We have 110 people to finish remaining 500
who will finish it in 500/110 days
total days = 100 + 50/11

thanks .I made a mistake in calculation.edited it now.

gmatmachoman wrote:50 persons can complete the work in 100 days. In how many days will the work be completed if 10 persons start the work and 10 person join after every 10 days?

in one day, 50 persons complete 1% of the work and a single person completes 1/50 % OR .02% of the work.

in 10 days 10 persons will complete 2% of the work.
in next ten days 20 persons will complete twice this i.e 4% of the work
in next 10, 30 persons will complete 6%

therefore, the total work done in intervals of 10 days becomes :

2+4+6+8+.....

sum of this Arithmetic progression till 9th term 90 = 90

on the 91st day, we have 100 persons working on the job, who complete 2% of the job/day. So, we need 5 more days to have the work completed.

IMO 95 days is the answer.

in ajith's solution, there are few points which are not clear to me :

ajith wrote:till 10th 10 days work worth 4500 man days would be done

We have 110 people to finish remaining 500
who will finish it in 500/110 days
total days = 100 + 50/11

"till 10th 10 days" means 90 days are over. So, while calculating the total days in the end it should be 90+ something.

moreover, on the 91st day we have 100 people not 110, the remaining fraction of work is 500/100.

Please correct me if I'm wrong.

Is this the entire question?

The only reason I ask is because you couldn't really give an solid answer as the question is written. In the solutions above there is an assumption that all the workers are working at an equal and constant rate. The question does not tell us to make this assumption.

The reason this is an issue is what if 20% of the workers did 80% of the total work (some workers more efficient than others)? It would then be very relavent to know when those workers were added. More importantly you need to know the rate at which each individual worker worked to answer this questions with any certaintly, if the question does not state that all workers work at and equal and constant rate.

Thanks,

Jared

sk818020 wrote:Is this the entire question?

The only reason I ask is because you couldn't really give an solid answer as the question is written. In the solutions above there is an assumption that all the workers are working at an equal and constant rate. The question does not tell us to make this assumption.

The reason this is an issue is what if 20% of the workers did 80% of the total work (some workers more efficient than others)? It would then be very relavent to know when those workers were added. More importantly you need to know the rate at which each individual worker worked to answer this questions with any certaintly, if the question does not state that all workers work at and equal and constant rate.

Thanks,

Jared

yes, you're correct. To solve this question, assumptions should be made. But, all these are assumptions,
are given as facts in the question itself which in normal cases. So, it doesn't hurt to assume general working efficiencies as same and start working on the numbers.

However, there is a BIG assumption that the workers can be more than 50. The first sentence says the work can be done by 50 workers in 100 days. So, someone might think that is the total number of persons who can work on the job. Answer in that case would be different.

harshavardhanc wrote:

sk818020 wrote:Is this the entire question?

The only reason I ask is because you couldn't really give an solid answer as the question is written. In the solutions above there is an assumption that all the workers are working at an equal and constant rate. The question does not tell us to make this assumption.

The reason this is an issue is what if 20% of the workers did 80% of the total work (some workers more efficient than others)? It would then be very relavent to know when those workers were added. More importantly you need to know the rate at which each individual worker worked to answer this questions with any certaintly, if the question does not state that all workers work at and equal and constant rate.

Thanks,

Jared

yes, you're correct. To solve this question, assumptions should be made. But, all these are assumptions,
are given as facts in the question itself which in normal cases. So, it doesn't hurt to assume general working efficiencies as same and start working on the numbers.

However, there is a BIG assumption that the workers can be more than 50. The first sentence says the work can be done by 50 workers in 100 days. So, someone might think that is the total number of persons who can work on the job. Answer in that case would be different.

Well, generally speaking, all the questions are hypotheticals, but I've never seen a quant GMAT question where you had to make any further assumptions to get the answer. All the information you need should be in the question stem. I getting at that typically you won't see a question like this on the GMAT.

Thanks,

Jared