Question

a number of being divided by 5 and 7 respectively leaves the reminder 2 and 4 respectively. find the reminder when the same number is divided by 35 ?

Answer 1

let number is x then
x/5 = y+2 ------> x= 5y+10 ---(1)
x/7 =y+4 ------> x= 7y +28 ----(2)
subtracting EQ (1) from (2)
we get 2y +18 =0
y= -9
put y= -9 in (1)
we get x = -35
when we divide -35 by 35
we get quotient = -1 and remainder 0