Question

A two digit number is such that the product of its digits is 20. if nine is added to the number the number is reversed , find the number

Answer 1

Hey

Here is your answer,

the two-digit number = 10x + y
and reversed number = 10y + x

given -

xy = 20 --------------1
and 10x + y + 9 = 10y + x ---------------2

Solve equation 2

10x + y + 9 = 10y +x
9y - 9x = 9
y - x = 1
y = 1 + x ---------------3

substitute equation 3 in equation 1

xy = 20

x (1 + x) = 20
x^2 + x - 20 = 0

Solve this quadratic equation....

x^2 + 5x - 4x - 20 = 0
x(x + 5) - 4 (x + 5) = 0
(x + 5) (x -4) = 0
x = -5 and x = 4

As required number is positive two digit number, consider x = 4

Therefore, xy = 20  y = 20/x  y = 20/4 = 5
therefore, the two digit number = 10x + y = 10*4 + y = 45.
Here
Hope it helps you!