Question

The sum of the digits of a 2-digit number is 7 . The number obtained by interchanging the digits exceeds the original number by 27 . Find the number.

Answer 1

Let Tens Place Digit=x

Let Unit Place Digit=y

Sum of Digits=7

Means

x+y=7

x=7-y

Original Number=10×Number at Tens Place +Number at Unit place

Original Number=10x+y

Reverse Number=10y+x

Reverse Number Exceeds Original Number(10x+y) by 27.

A/Q

Original Number+27=Reverse Number

10x+y+27=10y+x

27=10y+x-(10x+y)

27=10y+x-10x-y

27=9y-9x

27=9(y-x)

27/9=y-x

3=y-x

Y-X=3

We know

X=7-Y

Y-(7-Y)=3

Y-7+Y=3

2Y=3+7

2Y=10

Y=10/2

Y=5

WE KNOW

X=7-Y

X=7-5

X=2

Original Number=10x+y=10×2+5=25

$\boxed{\mathbf{\large{Original\:Number=25}}}$