Question

the sum of digits of a two digit number is 13. if the number subtracted from the one obtained by interchanging the digits the results is 45. what is the numbers

Answer 1

let two digit be ten's digit be x and and unit digit be y

so number = 10x + y


after interchanging number,

new number = 10y + x


according to question

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

9(x- y) = 45

x-y = 5 ..... (1)

as we have,

x + y = 13 ...... (2)

by solving (1) & (2) we get,

x = 8

y = 3

so number is 83


Hope it helps

Answer 2

Let the number be 10x+y
A.T.Q
x+y=13....................(i)
10y+x-10x-y=45
9y-9x=45
y-x=5.......................(ii)
Solving the equations.(i) and (ii)
y=9
x=4
number =10x+ y
              =40+9
               =49