Question

a number has two digit whose sum is 6 on adding 18 to the number its digits are interchanged .the number is ?

Answer 1

Let our two digital number be xy

Equation1: x+y=6.

Equation1: xy+18=yx

10x+y+18=10y+x

9x-9y=-18

x-y=-2.

Now we will equate value of x and y from both equations

x-y=-2

x+y=6

Add both

2x=4

x=2 and then 2+y=6 i.e. y=4

So our number xy is 24 and when added 18 then new number is 42

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Answer 2

let no. be 10x +y
A/q x+y=6
10x+y= 10y+x -18
= 9(x-y)=-18
x-y= -2
and,x+y=6
so, 2x=4
x=2
x-y=-2
2-y=-2
so,y=4
no. is 24