Question

the sum of the digit of a 2 digit number is 10. if 36 is subtracted from the number, the digits interchange their places. find the number with linear equations in one variables​

Answer 1

Answer:

73

Step-by-step explanation:

Let the Unit digit be x

and ten's digit be y  

Original number :- 10y + x

Interchanged number :- 10x + y

• Sum of the digit is 10

x + y = 10  

x = 10 - y ....... ( i )

• If 36 is subtracted from the Number the digit interchanged their place  

10 y + x - 36 = 10 x + y

10y - y + x - 10x = 36

9y - 9x = 36

( Dividing by 9 )

y - x = 4

- x = 4 - y

x = -4 + y .... ( ii )

Equating ( i ) and ( ii )

 10 - y = - 4 + y

10 + 4 = y + y

14 = 2y

7 = y

 Putting the value of y in eq ( i )

x = 10 - y

x = 10 - 7

x = 3

So ,

Our required number is  

10y + x

= 10 × 7 + 3

= 70 + 3

= 73

Original number is 73 !!