Question

sum of the digits of a two-digit number is 9 when we interchange the digits it is found that the resulting number is greater than the original number by 27 what is the two digit number find ​

Answer 1

Answer:

Let the tens digit be x and ones digit be y.

ATQ.

x + y = 9 -----------(i)

Again,

10y + x = 10x + y + 27

9y - 9x = 27

y - x = 27/9

x - y = -3 --------(ii)

x + y = 9

x - y = -3

----------------

2x = 6

-----------

So [ x = 3 ]

x + y = 9

y = 9-3

[ y = 6 ]

Original Number = 10x + y

= 10(3) + 6

= 36

Answer 2

$\bold{\underline{\underline{\huge{\sf{ANSWER:}}}}}$

Given:

The sum of the digits of a two-digit number is 9,when we interchange the digits it is found that the resulting number is greater than the original number by 27.

To find:

The two-digit of number.

Explanation:

Let the unit's digit be R &

Let the ten's digit be (9-R)

∴ The original number= 10(9-R)+R

→ 90 -10R+R

→ 90 -9R

&

On interchanging the digits:

New number= 10R+(9-R)

New number= 10R+9-R

New number= 9R +9

A/q

⇒ 9R+9=90-9R+27

⇒ 9R+9 =117-9R

⇒ 9R+9R=117-9

⇒ 18R= 108

⇒ R= $\frac{\cancel{108}}{\cancel{18}} =6$

⇒ R= 6

Putting the value of R in the original number.

Thus,

The original number is 10(9-6)+6

The original number is 90-60+6

The original number is 30+6

The original number is 36.