A number is 27 more than the number obtained by reversing its digits. If its unit’s and ten’s digit are $x$ and $y$ respectively, write the linear equation representing the above statement.

Given:

A number is 27 more than the number obtained by reversing its digits.

Its unit’s and ten’s digits are $x$ and $y$ respectively.

To do:

We have to write the linear equation representing the above statement.

Solution:

Unit’s digit $= x$

Ten's digit $= y$

This implies,

The given number $= 10y+x$

The number obtained by reversing the digits $=10x+y$

The number is 27 more than the number obtained by reversing its digits.

Therefore,

$(x + 10y) - (y +10x) = 27$

$x + 10y - y - 10x = 27$

$-9x + 9y = 27$

$-9(x-y) = 27$

$x-y=-3$

$x-y+3=0$

Hence the linear equation representing the given statement is $x - y + 3 = 0$.

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Updated on: 10-Oct-2022

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