Question

A TWO DIGIT NUMBER IS SUCH THAT THE PRODUCT OF ITS DIGITS 35.IF 18 IS ADDED TO THE NUMBER .THE DIGITS INERTCHANGING THEIR PLACE . FIND THE NUMBER

Answer 1

let the digits be x and y.
product = xy =35, x= 35/y
the no is 10x+y
on interchanging the digits the no becomes 10y+x
ATQ,
10x+y + 18= 10y + x
10x + y - 10y -x =-18
9x- 9y = -18
taking 9 common
9 (x-y)= -18
x-y = -18/9
x-y= -2 -----(1)
putting value of x in eq (1)
35/y-y =-2
taking LCM
35-y^2/y =-2
35-y^2=-2y
-2y+y^2-35=0
arranging in order
y^2-2y-35=0
on factorisation
y^2-7y+5y-35=0
on taking common
y(y-7) +5(y-7)=0
(y+5)(y-7)=0
y= -5,7
therefore x = 35/7=5
so the no. becomes
10*5+7=57
hope it helps you.