157. The product of digits of a 2-digitnumber is 24. If we add 45 toth

1.	157. The product of digits of a 2-digitnumber is 24. If we add 45 tothe number, the new number ob-tained is a number formed byinterchanging the digits.What isthe original number?(1) 54(3) 38(2) 83(4) 45
Answer» 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

157. The product of digits of a 2-digitnumber is 24. If we add 45 tothe number, the new number ob-tained is a number formed byinterchanging the digits.What isthe original number?(1) 54(3) 38(2) 83(4) 45

Answer»

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