Question

answer it ....given explain nation​

Answer 1

Given :-

• Sum of digits of the two-digit no. is 9.
• 27 is added to it, the digits of the number get reversed.

Have to Find :-

• What's the original number.

Solution :-

Let the first digit be " a "

The second two-digit no. be " b "

So the orginal two-digit number will be (10a + b)

The reversing number be (10b + a).

Now, As we know from the given that the sum of digits is 9 , then

• ⠀⠀⠀a + b = 9. ...... ⠀ Eq(1)

Then, it is also said in the Question that after adding 27 in the original number then it form digits of the number interchanged.

So, According to the Question

(10a + b) + 27 = (10b + a) .......eq (2)

Solving it further ,

$:\implies \bf{27 = (10b + a) - (10a + b)}$

$:\implies \bf{27 = 10b + a - 10a - b}$

$:\implies \bf{27 = 9b - 9a}$

$:\implies \bf{27 = 9(b - a)}$

$:\implies \bf{\dfrac{27}{9} = (b - a)}$

$:\implies \bf{3 = (b - a)}$

$:\implies \bf{- a + b = 3}$

⠀⠀⠀$\bf{- a + b = 3}$ ⠀⠀Eq(3)⠀

Then, Equation (3) is formed .i.e, (-a + b = 3).

Taking the Equation (1) and (3) .

Solving it further by using the elimination method,

$\bf{a + b = 9}$

$\underline{\bf{- a + b = 3}}$

$\bf{2b = 12}$

Now , from this we will find the value of " b "

↬ 2b = 12

↬ b = 12/2

↬ b = 6

Therefore, Substituting the value of b in the equation (3)

⠀⠀⠀⠀⠀$\bf{-a + b = 3}$

⠀⠀⠀⠀⠀$:\implies \bf{-a + 6 = 3}$

⠀⠀⠀⠀⠀ $:\implies \bf{-a = 3 - 6}$

⠀⠀⠀⠀⠀ $:\implies \bf{-a = -3}$

⠀ $:\implies \bf{a = 3}$

The value of a → 3.

Thus , as we assume the original number → (10a + b), according to the question.

Now, Simply putting the value of a and b.

10a + b

=> 10 × 3 + 6

=> 30 + 6

=> 36

Thereby, the Orginal number is 36.