The sum of a two digit number and the number obtained by reversing the digits is 66. If the digits of the number differ by 2, find the number. How many such numbers are there?

Question no 28

The sum of a two digit number and the number obtained by reversing the digits is 66. If the digits of the number differ by 2, find the number. How many such numbers are there? class 10 maths standard chapter 3 Pair of linear equations in two variables

Solution:-

Let the ten’s and the unit’s digits in the first number be x and y, respectively.

 So, the original number = 10x + y

 When the digits are reversed, x becomes the unit’s digit and y becomes the ten’s

 Digit.

 So the obtain by reversing the digits= 10y + x

According to the given condition.

 (10x + y) + (10y + x) = 66

 i.e., 11(x + y) = 66

 i.e., x + y = 6 ---- (1)

We are also given that the digits differ by 2,

 therefore, either x – y = 2 ---- (2)

 or y – x = 2 ---- (3)

If x – y = 2, then solving (1) and (2) by elimination, we get x = 4 and y = 2.

 In this case, we get the number 42.

If y – x = 2, then solving (1) and (3) by elimination, we get x = 2 and y = 4.

 In this case, we get the number 24.

 Thus, there are two such numbers 42 and 24.

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