Question

the sum of the digits of a two digit number is 5 on adding 27 to the number it's digits are reversed find the original number​

Answer 1

Answer:

14 is the right answer

Step-by-step explanation:

14=1+4=5

14+27=41

Answer 2

Answer:

$\huge\tt\underline{Given}$

the sum of the digits of a two digit number is 5 on adding 27 to the number it's digits are reversed.

$\huge\tt\underline{to\:find}$

the original number

$\huge\tt\underline{solution}$

Let (x y) be the two digit number for which we are searching.

⭐ Then (x y) = 10x + y.

When you reverse the digits of the number, you get:

⭐ (y x) = 10y + x.

From the first sentence of the problem, we want the sum of the digits to be 5.That is,

⭐ x + y = 5 {Equation 1}

For the second sentence of the problem, we want:

⭐(10x + y) + 27 = (10y + x)

→ 10x + y + 27 = 10y + x {by just dropping the parentheses}

→ 9x - 9y = -27 {by subtracting 10y and x from both sides}

→ x - y = -3 {by dividing through by 9}

→ 2x = 2, {by adding the previous equation to Equation 1}

→ $\tt\underline\pink{x\: =\: 1}$

→$\tt\underline\pink{y\: =\:4}$ {since the sum of the digits equals to 5}

So the two digit number for which we are looking is 14.

As a check, if you add 27 to 14, you get 41.

$\huge{ \underline{ \underline{ \red{ \sf{ Answer :}}}}}$

hence, 14 is the original number