Question

A two-digit number is such that the product of its digits is 20. If 9 is added to the number, the digits interchange their places. Find the number.

Answer 1

Answer:

hey mate your ans is 45 and-54

Answer 2

Number is 45

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 = 20  

x = 20/y -------------(1)

10x + y +9 = 10y + x

9x - 9y = -9

Dividing by 9, we get x - y = -1 -------------(2)

Substituting x = 20/y in (2), we get: 20/y - y = -1

20 - y² = -y

y² - y -20 = 0

y² -5y +4y - 20 = 0

y (y - 5) + 4 (y - 5) = 0

(y + 4) (y -5) = 0

Y can be -4 or + 5

Substituting in equation 1, we get: x = -5 or +4

Taking the positive values of x and y, we get x = 4 and y = 5.

The number is 10x + y = 40 + 5 = 45