Question

The sum of digits of a two digit number is 15. If 9 is added to the number the digits are reserved .Find the number - linear equation in one variable

Answer 1

Step-by-step explanation:

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

So, the number will be 10x+y

According to the first condition-

⇒x+y=9 ....(1)

According to the second condition-

⇒10y+x=10x+y+27⇒9y=9x+27

⇒y=x+3 ...(2)

Put the value of y in (2), we have

⇒x+x+3=9

⇒x=3

⇒x+y=9

⇒3+y=9

⇒y=6

∴ the number is 36.

Answer 2

SOLUTION :-

Let,

Digit in ten's place = x

Digit in one's place = y

Two digit number = 10x + y

According to the first condition,

$\longrightarrow\sf x+y=15 \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ ............................(1)$

According to the second condition,

$\longrightarrow \sf 10x+y+9=10y+x \\\\\longrightarrow 10x-x+y-10y=-9 \\\\\longrightarrow 9x-9y=-9\\\\\longrightarrow x-y=-1 \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ ............................(2)$

Equation (1) + Equation (2),

$\longrightarrow \sf 2x= 14 \\\\\longrightarrow \bf x= 7$

Substitute x = 7 in equation (1),

$\longrightarrow\sf 7+y=15\\\\\longrightarrow y = 15-7 \\\\\longrightarrow \bf y = 8$

TWO DIGIT NUMBER = 78