the sum of the digits of a two digit number is 10 the number obtained by interchanging the digit exceeds the original number by 54 find the original number
Answers
GIVEN :
- The sum of the digits of a two digit number is 10.
- The number interchanging the digit exceeds the original number by 54.
TO FIND :
- The original number = ?
STEP - BY - STEP EXPLANATION :
NOTE :---- If the digit of a two digit number are x (ones) and Y (tens) then the required number is 10y + x example as -----» 10 × Tens digit + Ones digit
[ RECALL THAT
=> 25 = 10 × 2 + 5
=> 36 = 10 × 3 + 6 etc.]
Since, the required number is a two digit number so we will have to find its ones digit and its tens digit.
=>Let the digit at ones place be 'X'
it is given that the sum of digit of the number is 12.
Hence, the digit at ones place = 12-x
Thus, the original number
= 10 × ( 12 - x ) + x
= 120 - 10x + x
= 120 - 9x
onenter changing the digits of the given number the digit at ones place becomes (12x - x) and the digit at tens place becomes x.
New number = 10x + ( 12-x )
= 9x + 12
it is given that the new numbers exceeds the original number by 54.
i.e. New number – original number = 54
(9x + 12) – (120 – 9x) = 54
"OR'
9x + 12 – 120 + 9x = 54
→ 18x – 108 = 54
→ 18x = 54 + 108
→ 18x = 162
"OR"
=> X = 162/18 = 9
Hence, the digit at ones place = 9
the digit at tens place = ( 12 – 9 ) = 3
Original number = 39