Question

If the digits of a two-digit number are interchanged, the number so formed is 18 more than the original number. The sum of digits is 8. What is the thrice value of

original number?

Answer 1

Answer:

✪ The answer is 35.

Step-by-step explanation:

☘Answer:-

Given:-

• the sum of the digits is 8.

To find:-

• the thrice value of original number.

Solution:-

$Let \: \: the \: \: given \: \: number \: \: be \: \: xy$

$xy \: \: can \: \: be \: \: written \: \: as \: \: 10x + y$

$According \: \: to \: \: the \: \: given \: \: data,$

$xy \: = \: xy \: + \: 18$

$⇒ \: 10x \: + \: y = \: 10y \: + \: x \: + \: 18$

$⇒ \: 9y \: - \: 9x \: = \: 18$

$⇒ \: x \: - \: y \: = \: 2 \: - - - - - (1)$

$and \: \: also \: \: its \: \: given \: \: that \: \: sum \: \: of \: \: \\ digits \: \: = 8$

$⇒ \: x \: + \: y \: = \: 8 \: - - - - - (2)$

$solving \: \: equation \: \: (1) \: and\: (2) \: we \: \: get$

$\: \: \: \: \: \: x \: + \: y \: = \: 8 \\ \: \: \: \: \: \: \: \: \: x \: - \: y \: = \: - 2$

___________________

$\: \: \: \: \: \: \: \: \: \: \: \: \: \: 2x \: = \: 6$

$x \: = \: 3 \: \: and \: \: y \: = \: 5$

$Hence, \: \: the \: \: given \: \: number \: \: is \: 35.$