Question

2. The sum of the digits of a 2-digit number is 13. The number formed by interchanging the digits is 45 more than the original number. Find the original number. umber is​

Answer 1

The two digit of 2-digit number be x and y.

x+y=13⟶(i)

2-digit number =10x+y

2-digit number obtained by reversing the digits =10y+x

∴(10y+x)−(10x+y)=45

⇒9y−9x=45

⇒y−x=5⟶(ii)

On adding (i) and (ii),

2y=18

y=9

Putting y in equation (i), we get,

x+y=13

x=4

∴ 2-digit number =10x+y=49

Answer 2

Answer:

a+b=13⟹b=13−a

10b+a=10a+b+45

⟹9b=9a+45

⟹b=a+5

⟹13−a=a+5

⟹13=2a+5

⟹2a=8

a=4⟹b=9

The original number is 49.