Let the unit digit be ‘x’
Let the ten’s digit be ‘y’.
Original number will be
10x ten’s digit+ one’s digit
=10x+y
On interchanging of digits,
Let unit’s digit be ‘y’.
Let ten’s digit be ‘x’.
New number will be
10 x ten’s digit + one’s digit
=10y+x
According to question,
Product of digit of two digit number = 35
So, it becomes,
xy=35———–1
If we add 18 to the number the new number obtained is number formed by interchange of digits.
10x+y+18=10y+x
10x-x+18=10y-y
9x+18=9y
18=9(y-x)
18/9=y-x
2=y-x
y=2+x—————2
Put the value of eq(2) in Eq(1).
xy=21
x(2+x)=35
x^2+2x=35
x^2+2x-35=0
x^2+7x-5x-35=0
x(x+7)-5(x+7)=0
(x+7)(x-5)=0
x+7=0
x-5=0
x=-7 ,x=5
x=-7 will be rejected.
So, x=5 and
xy=35
5y=35
y=35/5
y=7
Hence, original number will be
10x+y=10×5+7=50+7=57
New number will be
10y+x=10×7+5=70+5=75
Therefore, Numbers are 57 and 75.