Question

Give Ans.of question no 12

Answer 1

let the number be 10x+y
xy=20
10x+y+9=10y+x
x-y=-1
y=x+1
x(x+1)=20
x^2+x=20
x^2+x-20=0
x^2+5x-4x-20
x(x+5)-4(x+5)
(x+5)(x-4)
x=-5(neglecting because it can't be -ve)
x=4
xy=20
y=5
the number =10x+y=45

Answer 2

let the numbers x and y
xy = 20
since x and y are at tens and one place respectively
so we can write as
digits = 10x+y
after adding 9 it interchanges
so
the interchanged digit can be written as 10y+x
now
10x+y+9=10y+x
9x+9=9y
x+1=y
y-x=1.....(1)
now
(y-x)^2=y^2+x^2-2yx
y^2+x^2=41
now
(y+x)^2=y^2+x^2+2yx
(y+x)^2=81
(y+x)= 9....... (2)
adding (1) and (2)
2y=10
y=5
so x= 20/5=4

so the digit is 45.
thanks for the question.
hope it will help you.