Question

a two digit number is such that the product of its digits if 18. when 63 is subtracted from the number the digits interchange their places find the number?

Answer 1

let digit be XY

X× Y = 18

XY -63 = YX

10 X + Y - 63 = 10 Y +X

9 X - 9 Y - 63 = 0

X - Y-7 = 0

X × Y = 18

X = 18/Y

18/Y - Y -7 = 0

18 - Y.Y - 7 Y = 0

- Y.Y+2y - 9 y + 18 =0

-y ( y -2) -9(y-2) = 0

y = 2

x = 18/2 = 9


SO 92

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