Question

The sum of the digits of a two digit number is 9 When the digits are reversed the number increases by 9. Find the number.

Answer 1

Answer:45

Explanation:

Let the unit place be ‘x'

Tenth place be y

The number is 10y+x

x+y = 9 (according to the condition) (1)

Digits are interchanged Unit place' y ‘& tenth place ‘ x'

New no is 10x +y

This is 9 more than the original number

10x+ y = 10y+x +9

10x-x+y-10y = 9

9x-9y= 9

x-y = 1 (dividing by 9) (2)

Adding the two equations

2x = 10

x= 5

Substituting the value of x in first equation

y = 4

The number is 45, the original number is 54 this is 9 more of the new number.

Ans :45