Question

the difference of 2 numbers is 642.when the greater number is divided by the smallest number,the quotient is 8 &the remainder is 19 .find the numbers

Answer 1

Answer:

Greater no. is 553 & smaller no. is 89

Step-by-step explanation:

let the two numbers be: a & b

:

the difference between two numbers is 642.

a - b = 642

or

a = b + 642

:

when the greater is divided by the smaller the quotient is 8 and the remainder is 19.

%28%28a-19%29%29%2Fb = 8

multiply both sides by b

a - 19 = 8b

replace a with (b+642)

b + 642 - 19 = 8b

b + 623 = 8b

623 = 8b - b

7b = 623

b = 623%2F7

b = 89

a = 642 - 89

a = 553

Answer 2

Answer : 731 and 89

Solution :
_________

Let, the numbers are x and y

Given that : Difference between numbers = 642

According to the question :

x–y = 642 ....(1)

Also given that : The quotient is 8 and remainder is 19 when largest number is divided by smallest one.

Now, according to the question :

$8y + 19 = x \\ \\ = > x - 8y = 19 \\ \\ = > x - 8(x - 642) = 19 \: \: \: \: \: [ From \: equation \: (1) ] \\ \\ = > x - 8x + 5136 = 19 \\ \\ = > 7x = 5117 \\ \\ = > x = \frac{5117}{7} = 731$

So, the largest number will be 731

And

$731 - y = 642 \\ \\ = > y = 731 - 642 \\ \\ = > y =89$

So, the smallest number will be 89