Question

A number consists of two digits whose sum is 12 if 18 is added to the number the digit are reversed find the number.

Answer 1

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Answer 2

Concept

A linear equation in two variables is an equation having degree 1 and variables two

For example x and y are the two variables

Given

Given that A number consists of two digits whose sum is 12 if 18 is added to the number the digit are reversed

Find

We need to find the numbers

Solution

Let the two digit numbers be 10y + x

The sum of two digits = x+ y

If the number is reversed than digits is 10x+y

Now the equation formed according to the statement.

x + y=12 - (1)

Now if 18 is added to it the digits are reserved than the equation formed is

10y + x - 18 = 10x + y

9y - 18 = 9x

9y - 9x = 18

9(y - x) = 18

y - x = 2 - (1)

Now x + y = 12 - (2)

(1) - y = 2 + x

Substitute in eq 2

x + 2 + x = 12

2x =10

x = 5

Now,

y = 2 + x

y = 2 + 5

y = 7

Hence the two digit number is 57

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