Question

the sum of digits of a 2 digit number is 8. the number obtained by interchanging the digits exceeds the given number by 18.find te given number.

Answer 1

Answer :

The required number is 35.

Step-by-step explanation :

Let the number at one's place be x and digit at ten's place be y.

Given, x + y = 8

⇒ x = 8 - y         .... (i)

Original number = 10 x + y

After interchanging digits = 10 y + x

According to the question ;

10 x + y + 18 = 10 y + x

⇒ 10 x - x + 18 = 10 y - y

⇒ 9x + 18 = 9 y

⇒ 9 ( y - x ) = - 18

⇒ y - x = - 18 / 9

⇒ y - x = - 2

⇒ - x = - 2 + y

⇒ x = y - 2       .... (ii)

On comparing (i) and (ii),

⇒ y - 2 = 8 - y

⇒ y + y = 8 + 2

⇒ 2 y = 10

⇒ y = 10 / 2

⇒ y = 5

Putting the value of y in eqⁿ (i)

x + y = 8

⇒ x + 5 = 8

⇒ x = 8 - 5

⇒ x = 3

Original number = 10 x + y

= 10 × 3 + 5

= 30 + 5

= 35

Hence, the required answer is 35.

Answer 2

$\underline{\underline{\mathfrak{\Large{Solution : }}}}$



$\textsf{Let the ones place digit is x and tens} \\ \textsf{ place digit is y.}$


$\mathsf{So, Number \: = \: 10y \: + \: x}$



$\underline{\textsf{According to question : }} \\ \\ \sf \implies x \: + \: y \: = \: 8 \qquad...(1) \\ \\ \textsf{And,} \\ \\ \textsf{Number obtained by interchanging the} \\ \textsf{digits = 10x + y .}$




$\underline{\textsf{Now,}} \\ \\ \sf \implies ( 10x \: + \: y ) \: - \: ( 10y \: + \: x ) \: = \: 18 \\ \\ \sf \implies 10x \: + \: y \: - \: 10y \: - \: x \: = \: 18 \\ \\ \sf \implies 9x \: - \: 9y \: = \: 18 \\ \\ \sf \implies 9(x \: - \: y ) \: = \: 18 \\ \\ \sf \implies 9(x \: - \: y) \: = \: 18 \\ \\ \sf \implies x \: - \: y \: = \: 18 \: \div \: 9 \\ \\ \sf \implies x \: - \: y \: = \: 2 \qquad...(2)$




$\underline{\textsf{Add (1) and (2) , }} \\ \\ \sf \implies x \: + \: \cancel{y }\: + \: x \: - \: \cancel{ y} \: = \: 2 \: + \: 8 \\ \\ \sf \implies 2x \: = \: 10 \\ \\ \sf \implies x \: = \: 10 \: \div \: 2 \\ \\ \sf \: \: \therefore \: \: x \: = \: 5$



$\underline{\textsf{Substitute the value of x in (1) , }} \\ \\ \sf \implies x \: + \: y \: = \: 8 \\ \\ \sf \implies 5 \: + \: y \: = \: 8 \\ \\ \sf \implies y \: = \: 8 \: - \: 5 \\ \\ \sf \: \: \therefore \: \: y \: = \: 3$



$\underline{\textsf{Now,}} \\ \\ \sf \implies Number \: = \: 10y \: + \: x \\ \\ \sf \qquad \: \qquad \qquad = 10 \: \times \: 3 \: + \: 5 \\ \\ \sf \qquad \: \qquad \qquad = 30 \: + \: 5 \\ \\ \sf \qquad \qquad \: \qquad = 35$