Question

the tens digit of a two digit number exceeds the units digit by5 . if the digite are reversed the new number is less by 45.if the sum of the digitbe 9.find the number

Answer 1

First number
10 (x)+1(9-x)
On interchanging
New number
10 (9-x)+1 (x)
Answer 90-9x+45=9x+9
126-9x=9x
126/18=x
7=x
Number 70+2
72

Answer 2

Hey

Here is your answer,

Let the units digit be y.

and the tens digit be x.

The number will be 10x+y.    --------- (1)

The reversed number will be 10y + x.   --------- (2)

Given, x + y = 9   -------------- (3) 

Solve (1) and (2) with the given number, we get

(10x + y) - (10y + x) = 45

10x + y - 10y - x = 45

9x - 9y = 45

9(x - y)=45

x- y = 45   ------------- (4)

on solving (3) and (4)  we get,

2x = 14

x = 7

Substitute x = 7 in (3)

y = 2.

Hence the original number will be 72.

Hope it helps you!