Question

A two-digit number is such that the product of the digits is 8. When 18 is subtracted to the number, then the digits are reversed.

Answer 1

Answer:

Step-by-step explanation:

Let the two digit number be 10x + y

Given : product of its digits(x y) = 8

x y = 8..(1)

When 18 is subtracted from the number, the digits interchange their places

10x + y - 18 = 10y + x

10x + y - 10y - x = 18

9x - 9y = 18

9(x - y) = 18

x - y = 18/9

x - y = 2

x = 2 + y……………….(2)

Put this value of x in equation 1.

x y = 8

(2 + y)y = 8

2y + y² = 8

y²  + 2y - 8 = 0

y² +  4y - 2y - 8 = 0

[By middle term splitting]

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

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

(y - 2 ) = 0   or ( y + 4) = 0

y = 2  or y = - 4

Since, a digit can't be negative, so y ≠ - 4.

Therefore , y = 2

Put this value of y in equation 1,

x y =8

x× 2 = 8

x = 8/2 = 4

x = 4

Required number = 10x + y  

= 10(4) + 2

= 40 + 2

Required number = 42