The sum of a two digit number and the number obtained by reversing the order of its digits is 121. If units and ten’s digit of the number are $x$ and $y$ respectively, then write the linear equation representing the above statement.

Given:

The sum of a two-digit number and the number obtained by reversing the order of its digits is 121.

The units and ten’s digit of the number 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 sum of a two-digit number and the number obtained by reversing the order of its digits is 121.

Therefore,

$(10y + x) + (y +10x) = 121$

$x + 10x + y + 10y = 121$

$11x + 11y = 121$

$11(x+y) = 121$

$x+y=11$

$x+y-11=0$

Hence the linear equation representing the given statement is $x + y - 11 = 0$. 

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Updated on: 10-Oct-2022

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