Question

if a number when divided by 82 the remainder is 81 and when divided by 72 the remainder is 71.find the number

Answer 1

guess division no is y
then as formula,
                           82*y+81=72*y+71
                        or,82y-72y=71-81
                        or,10y= -10
                        or,y= -10/10= -1

so,82(-1)+81=72(-1)+71
   or,-82+81= -72+71 [as y= -1 ]
   or,-1= -1
 so, the no is = -1