Question

the sum of the digits of a two-digit number is 11.the number got by interchanging the digits is 27 more than the original number what is the number?​

Answer 1

Answer

• The original number = 47.

Given

• The sum of digits of a two digit number is 11.
• The number got by interchanging the digit is 27 more than the original number.

To Find

• The original number.

Step By Step Explanation

Assumption :

Let the tens and ones digit number be x and y respectively.

Then there sum will be x + y = 11 => y = 11 - x. eq. 1.

Original Number = 10x + y.

Number formed by interchanging it's digits = 10y + x.

Equation :

Number formed by interchanging the digit is 27 more than the original. So equation will be ⤵

$\red \bigstar\: \: \: \: \: \underline{ \boxed{ \bold{ \purple{(10y + x) - (10x+ y) = 27}}}}$

Solution of Equation :

Let us solve the above equation.

$\longmapsto \tt(10y + x) - (10x+ y) = 27 \\ \\ \longmapsto \tt 10y + x - 10x - y = 27 \\ \\ \longmapsto \tt9y - 9x = 27 \\ \\ \longmapsto \tt9(y - x) = 27 \\ \\ \longmapsto \tt y - x = \cancel\cfrac{27}{9} \\ \\ \longmapsto \tt y - x = 3 \\ \\ \bold{ from \: eq.1 \downarrow} \\ \\ \longmapsto \tt(11 - x) - x = 3 \\ \\ \longmapsto \tt 11 - x - x = 3 \\ \\ \longmapsto \tt11 - 2x = 3 \\ \\ \longmapsto \tt 11 - 3 = 2x \\ \\ \longmapsto \tt8 = 2x \\ \\ \longmapsto \tt \cancel \cfrac{8}{2} = x \\ \\ \longmapsto \underline{\boxed{\bold{ \green{4 = x}}}} \: \: \: \: \: \: \: \purple\bigstar \\ \\ \tt y - x = 3 \implies \: \underline{\boxed{ \bold{ \pink{y = 7}}}} \: \: \: \: \: \purple\bigstar$

Therefore, the original number will be 10x + y => 47.

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