Question

A number consist of two digit whose sum is 6 .if 18 is added to the number, its digits are reversed . find the number​

Answer 1

24 is the answer bro

Answer 2

Given :

• A number consist of two digit whose sum is 6 . If 18 is added to the number, its digits are reversed. Find the number.

Solution :

Let's assume the ones digit as x .

Then, the tens digit will be (6 – x).

$\\ \\ \tt \therefore \: \: \: \: \: \: Number = 10(6 - x) + x \\ \\ \\ \tt \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = 60 - 10x + x \\ \\ \\ \: \: \: \: \: \: \: \: \: \: \tt \: = 60 - 9x$

Numbers obtained by reversing the digit :

$\\ \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \tt \: = 10x + (6 - x) \\ \\ \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \tt \: = 10x + 6 - x \\ \\ \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \tt \: = 9x + 6 \: \: \: \: \: \: \: \: \:$

Now, According to the question :

• Number + 18 = Number obtained by reversing its digits.

$\\ \tt : \implies \: 60 - 9x = 9x - 6$

• Transposing variables on one side and constant terms on other sides, we get :

$\\ \\ \: \: \: \: \: \tt \: - 9x - 9x = 6 - 60 - 18 \: \\ \\ \\ \tt : \implies \: - 18x = - 72 \: \: \: \: \: \: \: \: \: \\ \\ \\ \tt : \implies \: 18x = 72 \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ \\ \tt : \implies \: x = \frac{72}{18} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ \\ \tt : \implies \:{ \underline{ \boxed{ \mathfrak{ \pmb{ x = 4}}}}} \: \: \: \bigstar \: \: \: \: \: \: \: \: \: \: \:$

${\tt{The \: \: number \: \: is \: \: 60 - 9x }} \\ \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \tt = (60 - 9 \times 4) \\ \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \tt = 60 - 36 \\ \\ \: \: \: \: \: \: \: \: \: \: \: = {\frak {\pmb{24}}}$

• Hence, 24 is the required number.