A group of men decided to do a job in 6 days, but 18 men dropped out every day. If the job was completed in 8 days, then how many men initially decided to do the job.

252

Let initial number of men be M 

Total work = no. of men x days = 6M

Thus, the equation formed on this condition:

M + (M - 18) + (M - 36) .......... = 6M

Using the formula of sum in Arithmetic  Progression,

Sn = n/2[2a + (n − 1) × d]

Here, a = M, d = -18

$\frac{8}{2}$[2M + 7(-18)] = 6M

8M - 126 x 4 = 6M

2M = 504 or M = 252