Question

sum of the two digit number is 9. the number obtained by interchanging the digits exceeds the given number by 27. find the original number.

Answer 1

Let the digit on one's place be x
Let the digit on ten's place be y

The original number :- 10y+x

From the data :- x+y=9----------equation 1

Now if we interxhange the digit i.e.
let the digit on one's place be y
Let the digit on ten's place be x

The new number :- 10x+y

From the data :-10x+y = 10y+x+27
=10x-x=10y-y+27
=9x=9y+27
=9x-9y=27
=x-y=3--------------equation 2

Now adding equation 1 and equation 2
x+y=9
x-y=3
we will get 2x=12==>x=6

Substituting value of x in equation 1
x+y=9
y=9-6
y=3

ANSWER:-x=6 and y=3

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Answer 2

hi

let the number be xy

tens place = 10x

ones place = y

Sum of the two digit number is 9

x + y = 9.........[1]

the number obtained by interchanging the digits exceeds the given number by 27

so let

 form an equation

10 x +y = 10y +x + 27

10x +y -10y -x = 27

=>  9x - 9y= 27

let us divide by 9

=> x - y = 3.......[2]

on adding [1] and [2]

x + y =9

x - y = 3

2x = 12

x = 6

y = 9 -x

=> 9 - 6

=>3

x = 6 and y= 3

original no. = xy

=>63

hope it helps u

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