Question

sum of the two digits is 17, if we interchange the digits the new no. decreased by9 find the original number​

Answer 1

$\sf{\huge{SOLUTION}}$ :

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

Number = 10y + x

Sum of the digits, x + y = 17 ---> ( i )

( 10y + x ) - ( 10x + y) = 9

10y + x - 10 x - y = 9

9y - 9x = 9

y - x = 1 ---> ( ii )

Adding equation ( i ) and ( ii ),

x + y + y - x = 17 + 1

2y = 18

y = 9

Putting value of y in equation ( ii ),

y - x = 1

9 - x = 1

x = 9 - 1 = 8

Number = 10y + x = 10 ( 9 ) + 8

$\sf{\huge {Number \:=\: 98}}$