Question

the difference between two numbers is 642. When the greater is divided by the smaller , the quotient is 8 and the remainder is 19. Find the numbers.

Answer 1

let the two numbers be x,y

according to the question x-y=642...........(1)

and x=y(8)+19

x-8y=19..............(2)

(1)-(2)  then

x-y=642

x-8y=19

(-) (+)  (-)

7y=623

y=89

now, x-89=642

x=731

Answer 2

GIven that ,

Dividend is greater than Divisor by 642. Therfore , let,

                    Dividend = x + 642.  

                   Divisor = x  

                   Quotient = 8

                     Remainder = 19. We know that,

Dividend = Divisor × Quotient + Remainder. Therefore,

x+642 + X.8 + 19.

X + 642 = 8X + 19.

642 - 19 = 8X - X

7X = 623

X = 623/7

X = 89.

Therefore, Divisor = 89  

               Dividend = X+642=731.