An important question from linear equations in two variables as it was already asked in various examinations in which we have to find the numbers if the sum of the digits of a two-digit number is 12. The number obtained by interchanging the two digits exceeds the given number by 18.
RS Aggarwal, class 10, chapter 3E, question no 11
Let us consider,
One’s digit of a two digit number = x and
Ten’s digit = y
So, the number is x + 10y
By interchanging the digits,
One’s digit = y and
Ten’s digit = x
Number is y + 10x
As per the statement, x + y = 12………. (1)
y + 10x = x + 10y + 18
y + 10x – x – 10y = 18
x – y = 2 …(2)
Adding (1) and (2),
we have 2x = 14
or x = 7
On subtracting (1) from (2),
2y = 10
or y = 5
Answer: Number = 7+10×5 = 57