Question

The sum of 2 digits of a number is 9.if 27 is subtracted from the number then digits interchange their places.find the number

Answer 1

$\bf\huge\color{red}{ANSWER}$

→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

Solution :

Let tens place digit = x

units place digit = 9 - x

The number = 10x +( 9 - x )

= 9x + 9 ---( 1 )

Reverse the digits we get new

number = 10( 9 - x ) + x

= 90 - 10x + x

= 90 - 9x ----( 2 )

According to the problem given ,

9x + 9 - 27 = 90 - 9x

=> 9x + 9x = 90 - 9 + 27

=> 18x = 108

=> x = 108/18

=> x = 6

Therefore ,

Required number = 9x + 9

= 9 × 6 + 9

= 54 + 9

= 63

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