20 men can complete a piece of work in 15 days. One man starts the work and after every day one more man joins the work and this continues till the work is completed. Then, in how many days will the work be completed?
Answers
Answer:
Step-by-step explanation:
1 man one day work =1/20*15=1/300
After one n days finished
1/300+2/300+3/100+................+n/300=1
1+2+3+..........n=300
we know the formula
n(n+1)/2=300
n^2+n=600
n^2+n-600=0
n^2+25n-24n-600=0
(n-24)(n+25)=0
n=24,-25(neglect negative value)
Hence the work will be finished in 24 days.
Answer:
24 Days
Step-by-step explanation:
20 men can complete a piece of work in 15 days
1 man can complete work in 15 * 20 = 300 Days
1 man's 1 day work = 1/300
Work done of 1st Day = 1/300 ( 1 man on work
Work done on 2nd day = 2/300 ( 2 Men on work)
Work done on 3rd day = 3/300 ( 3 Men on work)
and so on
Let say work completed in n days then
1/300 + 2/300 + 3/300 +.................+ n/300 = 1
multiplying both sides by 300
1 + 2 + 3 +.......................+ n = 300
=> n (n+1)/2 = 300
=> n² + n = 600
=> n² + n - 600 = 0
=> n² + 25n - 24n - 600 = 0
=> n(n+25) -24(n+25) = 0
=> (n-24)(n+25) = 0
=> n = 24
Work will be completed in 24 Days