Question

A number consists of 2 digits whose sum is 9. if 27 is subtracted from the original number, the digits are interchanged. Then the original number is?

Answer 1

Hey there !!

→Let the ten's digit be x.

and, the unit's digit be y.

A/Q,

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

⇒ Original number = 10x + y.

⇒ Number obtained on interchanging = 10y + x.

→ Now, A/Q,

⇒ 10x + y - 27 = 10y + x.

⇒ 10x - x + y - 10y = 27.

⇒ 9x - 9y = 27.

⇒ 9( x - y ) = 27.

⇒ x - y = 3...........(2).

Now, substracte in eqyation (1) and (2), we get

x + y = 9

x - y = 3.

-  +    -

________

⇒ 2y = 6.

⇒ y = 3.

Put the value of y in equation (1), we get

⇒ x + y = 9.

⇒ x + 3 = 9.

⇒ x = 9 - 3.

⇒ x = 6.

Hence, the original number = 10x + y.

= 10 × 6 + 3.

= 63.

THANKS

#BeBrainly.

Answer 2

Heya!

Let the no be xy(form 10x + y)

A/Q ;

x+y = 9 eq1.

10x + y - 27 = 10y + x

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

=) 9x - 9y = 27

=) x - y = 3 eq2.

Add both eqs;

=) 2x = 12

=) x = 12/2 = 6

Put the value of y in eq2..

=) y = 9-6 = 3

Hence no is 63.

Hope it helps uh!!