Question

the sum of the digits of a 2-digit number is 8.The number obtain by interchanging the digits excreeds the given number by 18 . Find the given number

Answer 1

Let Tens Digit=X
Let Ones Digit=Y

A/Q
X+Y=8. (Equation 1)

Number=10×x+y
Number=10x+y

Why We Multiply 10 with x You have studied about Number System
MEANS Take Number 62
How 62 come
When=6×10+2=62

Just like Number=10x+y
Interchange Number=10y+x

A/Q
It Exceeds Original Number by 18

Then
10x+y+18=10y+x
10y+x-(10x+y)=18
10y+x-10x-y=18
9y-9x=18
9(y-x)=18. . (9 is common)
Y-X=18/9
Y-X=2

Y-X=2. (Equation 2)

Now Add Both Equation
$\: \: x + y = \: 8 \\ + y - x = + 2 \\ + x - x \: will \: cut \\ 2y = 10 \\ y = \frac{10}{2} \\ y = 5$
Taking Equation 1
x+y=8
x+5=8
x=8-5
x=3

Number=10x+y
10×3+5
35

Number=35