Question

the digits of a two digit number differ by 3.If the digits are interchanged and added to the original number the number obtained is 143. Find both the numbers.(use only one variable)

Answer 1

The answer is given below :

Since, the difference between the digits of the number is 3, we consider the numbers as (x + 3) and x at tens and ones place respectively.
where (x + 3) - x = 3.

Then, the number is

= 10(x + 3) + x

= 10x + 30 + x

= (11x + 30)

When the digits are interchanged, the number is

= 10x + (x + 3)

= (11x + 3)

By the given condition,

Original number + New number = 143

⇒ (11x + 30) + (11x + 3) = 143

⇒ 22x + 33 = 143

⇒ 22x = 143 - 33

⇒ 22x = 110

⇒ x = 110/22

⇒ x = 5

So, the digit at ones place is 5 and the digit is tens place is (5 + 3) = 8.

So, the numbers are 85 and 58.

Thank you for your question.