Question

The difference of two numbers is 642.
When the greater number is divided by
the smaller number, the quotient is 8 and
the remainder is 19. Find the numbers​

Answer 1

Answer:

Let x be the greater number and y be the smaller number.

Difference = x – y = 642 ……(1)

When the greater number is divided by a smaller number, the quotient is 8 and the remainder is 19.

According to Euclid’s division algorithm

Dividend = Divisor × Quotient + Remainder

x = y×8 + 19

x – 8y = 19 ……(2)

Subtracting equation (1) from equation(2),

7y = 623

y = 89

x – y = 642

x – 89 = 642

x = 731

Therefore, greater number is 731 and smaller number is 89

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.