Question

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.

Answer 1

Hint: The number formed using the information provided in question is \[10x + y\] . Now, reversing the digits of the number, we get a new number i.e. \[10y + x\] , which is 27 more than the original number.
So, to form a linear equation, subtract the original number equation from the new number equation which will be equal to 27.

Complete step-by-step answer:
It is given that, a two-digit number is formed in which the digit at unit’s place is x and the digit at ten’s place is y. The equation to form a number using the above information is 10y + x. … (1)
Now, it is said that the digits are interchanged, i.e. unit’s place is y and ten’s place is x.
So, the new equation formed is \[10x + y\] . … (2)
Now, it is given that the number obtained by interchanging is 27 more than the original number.
Thus, we have to subtract equation (1) from equation (2).
 $\therefore \left( {10x + y} \right)-\left( {10y + x} \right) = 27$
 $\therefore 10x + y-10y - x = 27$
 $\therefore 9x-9y = 27$
 $\therefore 9\left( {x-y} \right) = 27$
 $\therefore \;x-y = 3$
Thus, we get the equation as \[x-y = 3\] .

Note: A number can also be written as the sum of product of the digit and its respective place in that number. For example, a number has 3 at its ten’s place and 5 is at its unit’s place. So, multiplying the digits by their respective place i.e. 3 multiplied by 10 (3 $ \times $ 10) because it is at ten’s place and 5 multiplied by 1 (5 $ \times $ 1) because it is at unit’s place. Now, the sum of these will give the number i.e. \[(3\;10) + (5\;1) = 30 + 5 = 35\] .