Question

the sum of digit of a two digit number is 9.if 27 is subtracted from the number the digit are reversed. find the number

Answer 1

Hye mate..
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Let, the digits in the unit place be x

And the digits in the tens place be y

Thus,

The number is 10y + x

Given,

The sum of a two-digit number is 9

Which means,

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

Also,

If 27 is subtracted from the number the digit are reversed.

So,

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

=> 10y + x - 27 = 10x + y

=> 10y + x - 10x - y = 27 [ Interchanging their positions ]

=> 9y - 9x = 27

=> 9 ( y - x ) = 27

=> y - x = 3 ...(2)

Subtracting Eq.(2) from Eq.(1) we get,

=> ( x + y ) - ( y - x ) = 9 - 3

=> x + y - y + x = 6

=> 2x = 6

=> x = 6 / 2

=> x = 3

Putting the value of x = 3 in Eq.(1) we get,

=> 3 + y = 9

=> y = 9 - 3

=> y = 6

Hence,

The value of x and y are 3 and 6 respectively.

Now,

The number is 10(6) + 3

= 63

Hope it helps !!

Answer 2

hope this help you.