Question

a few workers were assigned a job of shifting 1855 bricks from one building to another in 7 days.after the first day,2 workers were removed from the job and thus everyday after first day,each worker had to shift 3 more bricks than the quota of the previous day. 1.find the total number of bricks shifted on the first day. 2.find the number of workers left on the last day

Answer 1

Number of workers on the first day: n
Number of total bricks to shift = 1855
Number of bricks shifted by each worker on day 1 = x

Number of bricks shifted on
 day 1 =  n x
 day 2 = (n-2) * (x + 3)
 day 3 = (n-4) * (x + 6)
 day 4 = (n-6) * (x + 9)
 day 5 = (n-8) * (x + 12)
 day 6 = (n-10) * (x + 15)
 day 7 = (n -12) * (x + 18) 

Total =>    7 n x - 42 x + 63 n - 546 = 1855
                 n x - 6 x + 9 n = 187          ---- (1)
factorize:
                 (n - 6) * ( x + 9) = 133 = 7 * 19

As 7 and 19 are both prime numbers, and  as x+9 cannot be 7,  
        n - 6 = 7   => n = 13
        x + 9 = 19   =>  x = 10

(1) First day 10 bricks were shifted.
(2) Number of workers on the last day = n - 12 = 1