The sum of the digits of a 2-digit number is 7. The number formed by reversing the digit is 45 more than the original number. Find the original number.
Answers
answer is 16
Step-by-step explanation:
▶ Given
i) The sum of the digits of a two digit number is 7
ii) The number formed by reversing the digit is 45 more than the original number
▶ Let :
i) Let the two digit number be 10x + y, where x and y are one's and ten's digits respectively
▶ According to the Question :
The sum of the digits of the number is 7
•°• x + y = 7 ....... ( i )
After reversing the digits, the number becomes 10y + x
The number formed by reversing the digit is 45 more than the original number
•°• 10y + x - ( 10x + y ) = 45
=> 10y + x - 10x - y = 45
=> 9y - 9x = 45
=> 9 ( y - x ) = 45
=> y - x = 5
=> x - y = - 5 ....... ( ii )
Adding eq ( i ) and ( ii ) , we get :
x + y = + 7
x - y = - 5
_____________________
2x = 2
x = 1
Substituting value of x in equation ( i ), we get :
x + y = 7
=> 1 + y = 7
=> y = 7 - 1
=> y = 6
•°• The number = 10x + y
= 10 × 1 + 6
= 10 + 6
= 16
✔✔ Hence, it is solved ✅✅