Question

a numder consists tow digits whose sum is 9 if 27 is subtracted from the number its digits are reversed . find the number​

Answer 1

hey there

hope my answer helps you

let the ones place of the digit be y

the tens digit be x

we know that,

the general form of a two digit number is 10 ( tens digit ) + ones digit

therefore,

let the original number be 10x + y

reversed number be 10y + x

given that ,

when 27 is subtracted from the original  number the digits are reversed

therefore,

10x + y - 27 = 10y + x

transposing the variable terms to L.H.S and the number to R.H.S

we get ,

( 10x - x ) + ( y - 10y ) = 27

9x - 9y = 27

9 ( x - y ) = 27

=> x - y = 27 /9

=> x - y = 3 ......(1)

it is given that the sum of the digits is 9

therefore ,

x + y = 9 ......(2)

adding equations (1) and (2)

we get

x - y + x + y = 9 + 3 ( -y and y gets cancelled )

2x = 12

x = 6

y = 9 - 6

y = 3

the original number = 10x + y

10 (6) + 3 = 63

hope my answer helps you

have a good day