Question

A two digit number is such that the product of it's digits is 18. When 63 is subtracted from the number the digits interchange their places. Find the number

Answer 1

unit digit=y
10th digit=x

xy=18
y=18/x----(1)

(10x+y)-(10y+x)=63
10x+y-10y-x=63
9x-9y=63
(x-y)=63/9
x-y=7-----(2)

substitute (1) in to (2)

x-(18/x)=7
x^2-18=7x
x^2-7x-18=0
it's a quadratic equation
x=9

y=2

Answer 2

$\huge\bf{Answer:-}$

Let p be the product and n be the number.

Product × Number = 18 Equation - (1)

$10 + n - 63 = 10n + p$

$9p - 9n - 63 = 0$

$9p - 9n = 63$

$p - n = 7 Equation - (2)$

$p = 7 + n$

Adding values of p for Equation - (1)

$7 + n × n = 18$

n² + 7n = 18

n² + 7n - 18 = 0

n² + 9n - 2n - 18 = 0

$n*n + 9 - 2*n + 9 = 0$

$n + 9*n - 2 = 0$

$n = -9$

$n = 2$

This negative values is not correct so,

2 = number

7 + 2 = 9 is the product

Therefore, product = 9

The Number =

$= 10*9 + 2 = 92$

Therefore, 92 is the two digit number