the ones digits of a2- digit number is twice the tens digit when the number fromed by reversing the digit is added to the original number. the sum is 99 find the original number
Answers
Answer:
Step-by-step explanation:
Let the two digits of the number be x and y.
x is ten's digit and y is one's digit.
Thus the number is 10x + y.
According to given conditions:
Ones digit is 2 times the tens digit, => y = 2x. --------------------- (1)
The number formed by reversing the digit is added to the original number. the sum is 99,
=> (10x + y) + (10y + x) = 99
=> 11x + 11y = 99
=> x + y = 9
=> x + 2x = 9 (∵ from (1), y = 2x)
=> 3x = 9
=> x = 3.
=> y = 2x = 2 * 3 = 6.
Thus the original number is 36.
Step-by-step explanation:
Let the tens digit be y and the ones digit be x.
The original number = 10y + x
The reverse number = 10x + y
It is given that ones digit is twice the tens digit :]
➳ x = 2y ............[Equation (i)]
According to question now,
➳ 10x + y + 10y + x = 99
➳ 11x + 11y = 99
➳ 11 (x + y) = 99
➳ x + y = 99/11
➳ x + y = 9
➳ y = 9 - x.........[Equation (ii)]
Now, Substituting equation (ii) in equation (i) we get :
➳ x = 2 (9 - x)
➳ x = 18 - 2x
➳ 3x = 18
➳ x = 18/3
➳ x = 6
Putting x = 6 in equation (ii) we get :
➳ y = 9 - x
➳ y = 9 - 6
➳ y = 3
Therefore,
The original number = 10y + x = 10(3) + 6 = 30 + 6 = 36