Question

the sum of the digits of a two digit number is 8.when the places of the digits are interchanged the new number so formed will be 18 more than previous one. find the number.​

Answer 1

Step-by-step explanation:

Let the no be = 10x + y

Therefore the new no is = 10y + x

(10y + x) - (10x + y) = 18

9y - 9x = 18

y - x = 2 ..........(i)

x + y = 8 ...........(ii)

adding (i) and (ii)

2y = 10

y = 5

therefore x = 3

therefore the no. is 35

Answer 2

AnswEr

The original number is 35

GivEn

• The sum of the digits of a two digit number is 8
• When the places of the digits are interchanged the new number so formed will be 18 more than the previous one.

To FinD

• The original number

SoluTion

Let us consider the digits of the two digit number be x and y respectively

Therefore , the number will be ,

$\rm \longrightarrow 10x + y$

According to question

$\rm \implies x + y = 8 \dashrightarrow (1)$

Again by question

$\rm\implies 10y + x = 10x+y +18 \\\\ \rm\implies 10y-y+x-10x = 18 \\\\ \rm\implies 9y - 9x= 18 \\\\ \rm \implies 9(y-x)= 18 \\\\ \rm\implies y - x = 2 \dashrightarrow (2)$

Adding (1) and (2) we have,

$\rm\implies x + y + y - x = 8+2 \\\\ \rm\implies 2y = 10 \\\\ \rm\implies y = 5$

Putting the value of y in (1) ,

$\rm \implies x + 5 = 8 \\\\ \rm\implies x = 3$

Thus , the required number is :

$\bf\hookrightarrow 10\times 3 + 5 \\\\ \bf\hookrightarrow 35$