Question

The sum of digits of a two digit number is 13. If the number is subtracted from the one obtained by interchanging the digits, the result is 45. What is the number ?

Answer 1

Let the original number be 10x + y and the number obtained by reversing its digits be 10y + x
x + y = 13                        .........(i)

10x + y - (10y + x) = 45
⇒9x - 9y = 45
⇒x - y = 5
⇒x = 5 + y                      ..........(ii)

Substituting (ii) in (i), we get
5 + y + y = 13
⇒ 2y = 8
⇒ y = 4
∴ x = 9
2-digit no. = 94

Answer 2

solutions:-

Let
The two digits be x and y.

Number is 10x + y 

x + y = 13 (given)

y = 13 – x --------------1

A/q

10y + x – (10x + y) = 45

9y – 9x = 45

y – x = 5 --------------2

putting the value of y from equation 1 in eqn 2

13 – x – x = 5

13 – 2x = 5

2x = 8

x = 4

y = 13 – 4 = 9

The two-digit number = 10x + y = (10 × 4) + 9 = 49.

Thanks