A number consists of 2 digits. Sum of the digits is 9. If 9 is subtracted from the number, the digits are reversed. Find the sum of the numbers.
Answers
Solution :-
Let the ones and tens digits of a number be x and y respectively.
Case I : Sum of the digits is 9.
=> x + y = 9
=> x = 9 - y ______(i)
Case II : 9 is subtracted from the number, the digits are reversed.
=> 10y + x - 9 = 10x + y
=> 10y - y + x - 10x = 9
=> 9y - 9x = 9
=> 9(y - x) = 9
=> y - x = 1
=> y - (9 - y) = 1 [from equation (i)]
=> y - 9 + y = 1
=> 2y = 10
=> y = 10/2 = 5
Substituting the value of y in equation (i),
x = 9 - 5 = 4
Answer : Number = 5 × 10 + 4 = 54
Answer:
The sum of the number is 54
Explanation :
Let the tenth digit is x and the unit digit is y.
The number is 10x + y
=> Reversed number is 10y + x
x + y = 9 .........(given)
10x + y - 9 = 10y + x
9x - 9y = 9
Dividing both sides by 9
x - y = 1 …….(I)
x + y = 9 ......(II) ......[Given]
solving these two equations we get ,
x = 5 & y = 4
The number is 10 × 5 + 4 = 54
Thus, the number is 54