Question

the sum of the digits of a two digit number is 10 the number obtained by interchanging the digits exceeds the original number by 36 find the original number

Answer 1

Answer:

37

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Step-by-step explanation:

Lat say number = xy

= 10x + y

after exchanging digits 10y +x

10y +x = 10x +y + 36

9y - 9x = 36

y - x = 4

x + y = 10

Adding both

2y = 14 so y = 7

x + 7 = 10 so x = 3

Number = 37

Answer 2

Answer:

Let unit place digit be x.

Ten's place digit=(10-x)

original number=x+10(10-x)=x+100-10x=-9x+100

Number obtained by interchanging the digits

=10x+10-x=9x+10

As per the question,

(9x+10)-(-9x+100)=36 ➪9x+10+9x-100=36

18x-90=36 ➪18x=90+36=126

x=126/18=7

Unit place=7

Ten's place=10-7=3

Required number=7+3×10=37