Question

15 men can complete a work in 280 days. They started the
work and after every 10 days, 15 additional men were
employed. In how many days the work was completed?

(a) 70 days

(b) 60 days

(c) 55 days

(d) 50 days

Answer 1

In 10 days 15 men will complete 1/28 th of work.
to simplify calculations lets keep 28 in denominator:
1st 10 days = 1/28 th of work<----15 workers
Next 10 days = 2/28 th of work<----30 workers(total = 3/28)
Next 10 days = 3/28 th of work<----45 workers(total = 6/28)
Next 10 days = 4/28 th of work<----60 workers(total = 10/28)
Next 10 days = 5/28 th of work<----75 workers(total = 15/28)
Next 10 days = 6/28 th of work<----90 workers(total = 21/28)
Next 10 days = 7/28 th of work<----105 workers(total = 28/28)
so the work gets completed in 70 days.
did u get this ??

Answer 2

how did u get 1/28

Answer 3

in 280 days ----> complete work
in 10 days ------> x work
280 x = 10
x = 1/28

Answer 4

10 days w/15: 1/28
10 days w/30: 2/28, add in the 1/28 for 3/28 complete

ok, for some reason that was hard to parse at first :) good job

Answer 5

was trying like
280 days-------15 men
=>1day-------15/280
so, 10 days------(15/280)*10 = 15/28

wr am wrong ?

Answer 6

(15/280) is NOT the number of days....
so for 10 days u cannot multiply that with 10.

Answer 7

Can you please elobrate it the way u r solving...i didn't get it yet.
280 x = 10
x = 1/28

Answer 8

ok, lets take 15 men as 1 quantity only...don't find for 1 men.
now 'those 15 men' can complete the work in 280 days.
So, 'those 15 men' will complete (1/280) th part of work in 1 day.
got this ? this is most important.
then in 10 days, 'those 15 men' can complete (10/280) = (1/28)th part of work.........................
ask if still in doubts.

Answer 9

Total Unit of Work = 280*15
280 days is required to complete 280*15 unit of work by 15 men.
Therefore, In 10 days work done by 15 men = 150 unit.
We know that
Effeciency = Work done * No of man days.

If the man days will increase the efficiency will increase keeping the work done constant.
Thus we can interperate that

In next 10 days work done by 15*2 men = 300 unit
In next 10 days work done by 15*3 men = 450 unit

Therefore final AP series will be

[150+300+450+ ... to n days] = 280*15*10

n/2[2*150 +(n-1)*150] = 280*150
n(n+1) = 280*2
Solving above n =70

Answer 10

in one day; 15 men do 1/280 of the work; therefore, in a 10 day span; 15 men can do 10/280 of the work (or simply 1/28)

1/28 done in the time unit of 10 days with 15 men
2/28 done in the next time unit of 10 days, with 15+15 guys
3/28 done in the next time unit of 10 days, with 3(15) guys
....
x/28 done in any given time unit of 10 days, with 15x guys

the summation of this gives us a total job completed as\[\sum_{x=1}^{n}\frac{x}{28}=1\]
\[\frac{1}{28}\sum_{x=1}^{n}x=1\]
\[\sum_{x=1}^{n}x=28\]
\[\frac{n(1+n)}{2}=28\]
\[n(1+n)=56\]
\[n+n^2=56\]
\[n^2+n-56=0\]
\[n=\frac{-1\pm\sqrt{1^2-4(-56)}}{2}\]
\[n=\frac{-1\pm\sqrt{225}}{2}\]
\[n=\frac{-1\pm15}{2}\]
\(n=-8~or~7\) time units of 10 days each; since -8 is impractical, id stick with 70 days