Question

A number consisting of two digits whose sum is 5. If we add 9 in the number, the digits are interchange

Answer 1

Answer:

Let the digits in the tens be x and ones place be y.

Hence the number is 10x+y

By reversing 10y+x

Sum of digit =5

⇒x+y=5⟶(i)

Also that when 9 is added to the number the digits get interchanged.

∴(10x+y)+9=(10y+x)

10x+y+9=10y+x=0

9x−9y=−9

x−y=−1⟶(ii)

Adding (i) &(ii) we get ,

⇒x+y=5

⇒x−y=−1

⇒2x=4

⇒x=2

Put x=2 in x+y=5

∴2+y=5

⇒y=3

Hence the number is : 123