Question

the sum of the digits of a two digit no is 5.on reversing the digits of the no it exceeds the original number by 9 find the original number​

Answer 1

Answer:

$\bf The\ original\ number\ is\ 23.$

Step-by-step explanation:

Well, this question is from the chapter Pair of linear equations in two variables.

Given

Let the digit at tens place be x and the number at units place be y.

And the number will be (10x+y)

So, the sum of the digits of a two digit no is 5.

So, ATE

x+y=5 --(1)

Also,

On reversing the digits of the number, it exceeds the original number by 9.

So, the number that we'll get on reversing on the digits is

(10y+x)

So, ATE

(10y+x)=(10x+y)+9

10y-y+x-10x=9

9y-9x=9

9(y-x)=9

y-x=1 --(2)

Adding eq. (1) and (2)

2y=6

y=3

Putting, y=3 in eq. (1)

x+3=5

x=2

So, the original number is (10×2+3)=(20+3)=23

Answer 2

Answer:

$\large{\underline{\boxed{\sf Required \: number = 23}}}$

Step-by-step explanation:

Let the digit at unit's place be x and the digit at ten's place be y.

∴ Original number = 10x + y

According to the question ;

⇒ 10x + y + 9 = 10y + x

⇒ 10x - x + y - 10y = - 9

⇒ 9x - 9y = - 9

⇒ 9(x - y) = - 9

⇒ x - y = $\sf \dfrac{-9}{9}$

⇒ x - y = - 1.... (i)

_______________________

Also, it is given that the sum of the digits of the two digit number is 5.

⇒ x + y = 5.... (ii)

On adding equation (i) and (ii) -

⇒ x - y + x + y = 5 - 1

⇒ 2x = 4

⇒ x = $\sf \dfrac{4}{2}$

⇒ x = 2

Putting the value of x in (i)

⇒ x - y = - 1

⇒ 2 - y = - 1

⇒ y = 2 + 1

⇒ y = 3

_______________________

∴ Original number = 10x + y

                               = 10 * 2 + 3

                               = 20 + 3

                               = 23

Hence, the required number is 23.