Question

The sum of the digits of a two digit number is 9 . Also nine this number is twice the number obtained by reversing the order of the digits. Find the number​

Answer 1

Given

• Sum of digits of two-digit number = 9
• 9(Original number) = twice the reversed number.

To find

• Original number = ?

Solution

Let the digit at unit's place be a & digit at ten's place b.

⇒ Original number = a + 10b

⇒ Reversed number = b + 10a

AccordinG to Question :

⇒ a + b = 9

⇒ a = 9 - b ------ Equation (1)

Case 2 :

⇒ 9(a + 10b) = 2(b + 10a)

⇒ 9a + 90b = 2b + 20a

⇒ 2b + 20a - 9a - 90b = 0

⇒ 11a - 88b = 0

Putting value from Equation (1)

⇒ 11(9 - b) - 88b = 0

⇒ 99 - 11b - 88b = 0

⇒ -99b = -99

⇒ b = -99/-99

⇒ b = 1

So, digit at ten's place = 1

Putting this value in Equation (1)

⇒ a = 9 - 1

⇒ a = 8

So, digit at unit's place = 8

Now finding the number :

⇒ Original number = 8 + 10(1)

⇒ Original number = 8 + 10

⇒ Original number = 18

Therefore,

∴ Original two-digit number = 18

Answer 2

Given,

• Sum of the digits of a two digit number is 9.
• Nine times this number is twice the number obtained by reversing the order of the digits .

To Find,

• The Two digit number .

Solution,

⇒Suppose the ten's digit place number be a

And , Suppose the one's digit place number be b

Therefore ,

• Two Digit number = 10a + b
• Reversing number = 10b + a

According to the First Condition :-

• Sum of the digits of a two digit number is 9.

$\implies \sf{a + b = 9}$

$\implies \boxed{\sf{ b = 9 - a}}$

According to the Second Condition :-

• Nine times this number is twice the number obtained by reversing the order of the digits .

$\implies \sf{9(10a + b ) = 2(10b + a)}$

$\implies \sf{90a + 9b = 20b + 2a}$

$\implies \sf{90a - 2a = 20b - 9b}$

$\implies \sf{88a = 11b}$

$\implies \sf{88a = 11(9 - a)}$

(Put the value of b from the First Condition)

$\implies \sf{88a = 99 - 11a}$

$\implies \sf{88a + 11a = 99}$

$\implies \sf{99a = 99}$

$\implies \sf{a = \dfrac{99}{99}}$

$\implies \boxed{\sf{a = 1}}$

Now Put the value of a in First Condition :-

$\implies \sf{ b = 9 - a}$

$\implies \sf{b = 9 - 1}$

$\implies \boxed{\sf{b = 8}}$

Therefore ,

$\boxed{\sf{\purple{Two \ Digit \ Number = 10a + b = 10(1) + 8 = 18}}}}$

$\rule{200}2$