Question

The ten’s digit of a two digit number exceeds the unit’s digit by 5.If the digits are reversed ,the new number is less by 45. If the sum of the digits is 9 , find the numbers?

Answer 1

Hint: Each statement of question gives us one equation. You can get the answer from the first and third statement only. We can use a second statement for cross verification.

Complete step-by-step answer:
Let x be the unit’s place digit and y be the ten’s place digit of the number.
The ten’s digit of a two digit number exceeds the unit’s digit by 5.
⇒\[y - x = 5\] …..eqn1
the sum of the digits is 9
⇒\[x + y = 9\] ……eqn2
Adding these two equations we get
\[
  y - x + x + y = 5 + 9 \\
  2y = 14 \\
  y = 7 \\
\]
And the value of \[x = 2\].
The original number is 72.
On reversing the digits we get 27.
Difference between them is \[72 - 27 = 45\]
This satisfies our second statement from question.
So, the numbers are 27 and 72.

Note: Unit’s place digit and ten’s place digit are different. So consider two different variables.
Reversing the digits is nothing but changing their place value.
 We can use the difference condition of reversed numbers also.
Remember they have asked for numbers and not the digits. If required, the digits are 2 and 7.