Question

A number consists of two digits whose sum is 8. if 18 is added to the number it's digits are reversed. Find the number​

Answer 1

Given:

• A two digit number whose sum is 8.
• If we add 8 to the no. it's digits are reversed.

Find:

• Find the number.

Solution:

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

Now,

The number be = 10x + y

Given,

In Question x + y = 8.......(i)

$\rm \implies 10x + y + 18 = 10y + x$

$\rm \implies 10x - x + 18 = 10y - y$

$\rm \implies 18 = 9y - 9x$

$\rm \implies 9(y - x) = 18$

$\rm \implies y - x= \frac{ \cancel{18}}{ \cancel{9}} = 2$

$\rm \implies y - x= 2.......(ii)$

Now, adding eq(i) and eq(ii) we get

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

$\rm \implies \cancel {x} + y + y \cancel{- x} = 8 + 2$

$\rm \implies 2y= 10$

$\rm \implies y= \frac{ \cancel{10}}{ \cancel{2}} = 5$

$\rm \implies y= 5$

Now, put y = 5 in eq(i)

$\rm x + y = 8$

$\rm \implies x + 5= 8$

$\rm \implies x = 8 - 5$

$\rm \implies x = 3$

Hence, the number will be = xy = 35

Answer 2

Step-by-step explanation:

Let one digit of the number be x , then its ten digits digits will be (8−x) .

So , given number =10(8−x)+x

=80−10x+x

=80−9x

Now if digits are reversed , then Number obtained

=10x+(8−x)

=10x+8−x

=9x+8

According to question

(80−9x)+18=9x+8

98−9x=9x+8

90=18x

x=5

⇒ given number =80−9x

=80−9×5

=80−45

=35

∴ the number is 35