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

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Given : -

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?

Required Answer : -

Let the number is 10x + y

yso x + y = 13 _ _(1)

_(1)New number is 10y + x

x∴10y + x − 10x − y = 45

45⇒9(y−x) = 45

45⇒ y − x = 5___(2)

From (1) & (2)

2y=18 y=9

5___(2)From (1) & (2) 2y=18 y=9so x=4

5___(2)From (1) & (2) 2y=18 y=9so x=4∴ the number is 49

Answer 2

Step-by-step explanation:

Let the one digit number be x

and ten digit number be y

$x + y = 13$

the number =

$10y + x$

reversing the number

$10x + y$

subtracting number we get

$10x + y - (10y + x) = 45 \\ 10x + y - 10y - x \\ 9x - 9y = 45$

put

$x = 13 - y$

$9x - 9y = 45 \\ 9(13 - y) - 9y = 45 \\ 117 - 9y - 9y = 45 \\ - 18y = 45 - 117 \\ - 18y = - 72 \\ y = \frac{ - 72}{ - 18} \\ y = 4$

put y =4

$x = 13 - y \\ x = 13 - 4 \\ x = 9$