## The sum of a two digit number and the number formed by reversing the order of digit is 66 if the two digits differ by 2, find the number by

Question

The sum of a two digit number and the number formed by reversing the order of digit is 66 if the two digits differ by 2, find the number by using one variable. How many such numbers are there​.

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4 weeks 2021-11-06T08:27:43+00:00 1 Answer 0 views 0 2 NUMBERS which are 24 and 42 . ExplanatioN :

## Given :–

• Sum of a two digit number and the its reversed form of its digit is 66 .
• The digits of that number differ by 2 .

## ToFind :–

• The numbers which can be made from those DiGiTS .

## SolutioN :–

Let the First digit of the Original Number be x and the Second digit be y .

→ According to the First Condition :-

⇒ 10x + y + (10y + x) = 66

⇒ 10x + y + 10y + x = 66

⇒ 10x + x + 10y + y =66

⇒ 11x + 11y = 66

⇒ 11(x + y) = 66

⇒ x + y = 66 ÷ 11

⇒ x + y = 6  ———-(1)

→ According to the Second Condition :-

⇒ x – y = 2

⇒ x = y + 2  ————(2)

⇨ Putting the Value of ‘x’ from Equation(2) in Equation(1) :-

➟ (y + 2) + y = 6

➟ y + y + 2 =6

➟ 2y = 6 – 2

➟ 2y = 4

➟ y = 4 ÷ 2

y = 2

⇨ Now putting this value of ‘y’ in Equation(2) :-

➠ x = 2 + 2

x = 4

So , we have the two digits as 4 and 2 .

∴ 2 Numbers can be formed from these 2 digits which are 42 and 24 .