Question

33 men can complete a work in some days and 24 men can complete the same work in 6 more days in how many days can 44 men complete the work​

Answer 1

Step-by-step explanation:

let ,

33 mens can do the work in "x" days

24 men can do the work in " x + 6 " daysb

than,

33x = 24( x + 6)

33x = 24x + 198

x = 16 days

Now,

33 men can do work in 16 days

1 man can do work in 16/33

44 men can do work in 16/33 *44= 12 days

Answer 2

Answer:

Number of man- days required to complete the work= 33 x 30= 990

Now on the first - day 44- men work and on the second day 43, and so on .

Sum of the Arithmetic Progression

Sn= n[2a + ( n-1)d]/2

here First term a= 44

Common Diff= d= -1

Sum = Sn=990

So===> 990= n[2x44 +(n-1) -1]/2

=n^2 -89n+1980= 0

=(n-44) (n-45)= 0

So n= 44 or 45. Here it can be only 44 ie (44+43+42+——- +1)= 990.

It has 44- terms and so the complete work will be done in 44- days.

[ ie on the first day 44- men will work and on the last day ie., on the 44- th day only one- man will work and thus 990 man- days work will be done] .