Question

Tell the answer of this question : if the sum of the digits of two digit no. is 9 the no. obtained by interchanging its digit and the original differ by 27 what is the original no.?

Answer 1

we can solve this question by linear equations in two variables

Answer 2

Let xy be the required two-digit number.

Let x be the number which is in unit's digit.

let y be the number which is in ten's digit.

Therefore the decimal expansion is 10x+y.

The number obtained by reversing the digits = 10y + x.   ------- (*)

Given that sum of two digit number is 9.

x + y = 9  ----- (1)

Given that Original number differ by 27.

10x + y = 10y + x + 27

10x + y - 10y - x = 27

9x - 9y = 27

x - y = 3    --------- (2)

On solving (1) and (2), we get

x + y = 9

x - y = 3
-------------
2x = 12

x = 6.

Substitute x = 6 in (1), we get

x + y = 9

6 + y = 9

y = 9 - 6

y = 3.

Substitute x = 6 and y = 3 in (*), we get

10y + x = 10(3) + 6

            = 30 + 6

            = 36.

Therefore the original number = 36.

Hope this helps!