Question

Product of digits of a 2-digit number is 24. If we add 45 to the number, the new number obtained is a number formed by interchange of the digits. What isthe number?

Answer 1

let the number is x + 10y
according to question ,
xy = 24 ----(1)

again,

x + 10y +45 = y + 10x

x - y = 5 --------(2)

solve equations (1) and (2)

x - 24/x = 5

x² -5x -24 =0

x = { 5±√25+96)}/2

=(5±11)/2

= 8, - 3

but x ≠ -3

so, x = 8 put this equation (2)
y = 3

so, the number is 8 + 30 = 38

Answer 2

let the 2 digit no be 10X+Y.
XY=24.........1
10X+Y+45=10Y+X..........2
from 1
24/X=Y
substitute this value in eq 2
hence we get ,
10X+24/X+45=(10*24)÷X+X
(10X²+24+45X)÷X=(240+X²)÷X
10X²+45X+24=X²+240
now by shifting
9X²+45X-216=0
Dividing by 9
X²+5X-24=0
X²-3X+8X-24=0
X(X-3)+8(X-3)=0
hence
(X+8)(X-3)=0
therefore
X=-8 or X=3
digit cannot be negative
hence X=3
put this value in equation 1
Y*3=24
therefore Y=8
hence the number is 10*3+8=38
hence the number is 38