Question

The ones digit of a 2-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. Find
the original number.
157​

Answer 1

Step-by-step explanation:

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

• The ones digit of a 2-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 one's digit of the number be x

The tens digit of the number be y

The original number = 10y + x

The reversed number = 10x + y

According to the 1st condition:-

The ones digit of a 2-digit number is twice the tens digit.

$\rm \implies x = 2y......(i)$

According to the 2nd condition :-

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

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

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

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

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)

$\rm \implies 2y+ y = 9$

$\rm \implies 3y = 9$

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

$\rm \implies y = 3$

Substituting y = 3 in equation (ii)

$\rm \implies x + y = 9$

$\rm \implies x + 3 = 9$

$\rm \implies x = 9 - 3$

$\rm \implies x = 6$

The original number

= 10y + x

= 10(3) + 6

= 30 + 6

= 36

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

Answer 2

Answer:

• 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