Question

A two-digit number is such that the product of its digits is 8. When 18 is subtracted from the number, the digits interchange their places. Find number.

Answer 1

Number is 42.

Step-by-step explanation:

Let x be the first digit and Y be the second digit of a two-digit number. The number will be 10x +y.

Given:

xy = 8

x = 8/y -------------(1)

10x + y -18 = 10y + x

9x - 9y = 18

Dividing by 9, we get x - y = 2 -------------(2)

Substituting x = 8/y in (2), we get: 8/y - y = 2

8 - y² = 2y

y² +2y -8 = 0

y² +4y -2y - 8 = 0

y (y + 4) -2 (y + 4) = 0

(y + 4) (y -2) = 0

Y can be 2 or 4

Substituting in equation 1, we get: x = 4 or 2

So the number is 42.