Question

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
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Answer 1

Step-by-step explanation:

$\bf\underline{\underline{\red{Given:-}}}$

• The ones digit of a two digit number is twice the tens digit.

• When the number formed by reversing the digits is added to the original number, the sum is 99.

$\bf\underline{\underline{\blue{To\:Find:-}}}$

• The original number.

$\bf\underline{\underline{\green{Solution:-}}}$

Let the tens digit of the number be x

The ones digit be y

The original number = 10x + y

The number obtained by reversing the digits = 10y + x

Case 1:-

The ones digit of a two digit number is twice the tens digit.

$\rm Once \:digit = 2(tens \:digit)</p><p></p><p>[tex]\rm \implies y = 2x.....(i)$

Case 2:-

Original number + Reversed number = 99

$\rm \implies (10x + y)+(10y + x) = 99$

$\rm \implies 10x + y+10y + x = 99$

$\rm \implies 11x + 11y = 99$

Dividing the whole equation by 11

$\rm \implies \dfrac{11x}{11} + \dfrac{11y}{11} = \dfrac{99}{11}$

$\rm \implies x + y = 9.....(ii)$

Substituting equation (i) in (ii)

$\rm \implies x + (2x)= 9$

$\rm \implies 3x= 9$

$\rm \implies x = \dfrac{9}{3}$

$\rm \implies x = 3$

Substituting x = 3 in equation (ii)

$\rm \implies x +y= 9$

$\rm \implies 3 +y= 9$

$\rm \implies y= 9-3$

$\rm \implies y= 6$

Now:-

The original number

= 10x + y

= 10(3) + 6

= 30 + 6

= 36

$\underline{ \boxed{ \purple{\bf \therefore The \: original \: number= 36}}}$

Answer 2

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