Question

The sum of the digits of a two-digit number is 9. If
27 is added to it, the digits of the number get
reversed. The number is
(1) 25 (2) 72 (3) 63 (4) 36​

Answer 1

Solution :

$\bf{\red{\underline{\underline{\bf{Given\::}}}}}$

The sum of the digits of a two digit number is 9. If the 27 is added to it, the digit of the number get reversed.

$\bf{\red{\underline{\underline{\bf{To\:find\::}}}}}$

The number.

$\bf{\red{\underline{\underline{\bf{Explanation\::}}}}}$

Let the ten's digit place be r

Let the one's digit place be m

So;

$\underline{\sf{The\:Original\:number=10r+m}}}}\\\underline{\sf{The\:Reversed\:number=10m+r}}}}$

A/q

$\mapsto\sf{r+m=9}\\\\\mapsto\bf{m=9-r..........................(1)}$

&

$\mapsto\sf{10m+r=10r+m+27}\\\\\mapsto\sf{10m-m+r-10r=27}\\\\\mapsto\sf{9m-9r=27}\\\\\mapsto\sf{9(m-r)=27}\\\\\mapsto\sf{m-r=\cancel{\dfrac{27}{9} }}\\\\\mapsto\sf{m-r=3}\\\\\mapsto\sf{9-r-r=3\:\:\:\:\:[from(1)]}\\\\\mapsto\sf{9-2r=3}\\\\\mapsto\sf{-2r=3-9}\\\\\mapsto\sf{-2r=-6}\\\\\mapsto\sf{r=\cancel{\dfrac{-6}{-2} }}\\\\\mapsto\sf{\pink{r=3}}$

Putting the value of r in equation (1),we get;

$\mapsto\sf{m=9-3}\\\\\mapsto\sf{\pink{m=6}}$

Thus;

The original number = 10r + m

The original number = 10(3) + 6

The original number = 30 + 6 = 36.

Answer 2

Option. 4). 36 is the correct option

Given :

• The sum of the digits of a two digits number is 9.

• 27 is added to it, the digits of the number get reversed.

To find :

• The new number =?

Step-by-step explanation:

Let the ones digit number of two digits of the number be x.

Then, the ten 's digit number of the two digit number be y.

Therefore, two-digit number is = 10x + y

And, the reversed number = 10y + x

According to the question :

➟ x + y = 9

➟ y = 9 – x ..... (1)

It is given that :

➟ 10y + x - 10x – y = 27

➟ 9y – 9x = 27

➟ 9(y - x) = 27

➟ y - x = 27/9

➟ y – x = 3 ..... (2)

Substitute the value of y from eq (1) in eq. (2)

➟ 9 – x – x = 3

➟ 9 – 2x = 3

➟ - 2x = 3 - 9

➟ - 2x = - 6

➟ 2x = 6

➟ x = 6/2

➟ x = 3

Hence, x = 3

So, y = 9 – x = 9 – 3 = 6

Therefore, the two-digit number is = 36.