Question

The sum of two digits of a number is 9. If 9 is subtracted from the number, then the digits are reversed. The number is:
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please tell me this​

Answer 1

Question:-

The sum of two digits of a number is 9. If 9 is subtracted from the number, then the digits are reversed. The number is

To Find:-

Find the number.

Solution:-

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

Given ,

x + y = 9 . . . . ( 1 )

The two numbers are:-

10y + x and 10x + y

According to the question:-

$\longrightarrow\sf \: 10y + x - 9 = 10x + y$

$\longrightarrow\sf \: 10y - y = 10x - x + 9$

$\longrightarrow\sf \: 9y = 9x + 9$

$\longrightarrow\sf \: 9y - 9x = 9$

$\longrightarrow\sf \: 9( y - x ) = 9$

$\longrightarrow\sf \: y - x = \cancel\dfrac { 9 } { 9 }$

$\longrightarrow\sf \: y - x = 1$ . . . . ( 2 )

Add equation ( 1 ) and ( 2 ):-

$\longrightarrow\sf \: y - x + x + y = 9 + 1$

$\longrightarrow\sf \: 2y = 10$

$\longrightarrow\sf \: y = \cancel\dfrac { 10 } { 2 }$

$\longrightarrow\sf \: y = 5$

Now ,

Substitute ' y ' value in equation

( 1 ):-

$\longrightarrow\sf \: x + y = 9$

$\longrightarrow\sf \: x + 5 = 9$

$\longrightarrow\sf \: x = 9 - 5$

$\longrightarrow\sf \: x = 4$

Hence ,

The number is 54

Answer 2

Thus the number is 54..

Let the digits at ones place be x

Then the digits at tens place=9-x - sum of two digits is 9)

Therefore the number =10 (9-x)+x=90-10x+x=90-9x

Now,Number obtained by reversing the digits=10x+9-x=9x+9

It is given if 9 is subtracted from the number.,it's digits are interchanged.

90-9x-9=9x+9

81-9x=9x+9

81-9=9x+9x

18x=72

x=72/18

x=4

digits at ones place is x=4

tens place=9-x=9-4=5

Thus the number is 54