Question

The sum of the digits of a two-digit number is 9. If 9 is added to the number formed by reversing
the digits, then the result is thrice the original number. Find the original number​

Answer 1

$\rm \mapsto \: \green{{ \underline{ \underline{answer \div }}}}$

=> Original number = 27.

$\rm \to \: { \underline{explanation \div }}$

=> Let the digit at ten's place be = x

=> Let the digit at unit place be = y

=> original number = 10x + y

=> reversing number = 10y + x

=> According to the question,

=> The sum of digit of two digit number = 9

=> x + y = 9 .....(1)

=> if 9 is added to the number formed by

reversing the digit then the result is thrice the

original number.

=> 10y + x + 9 = 3 ( 10x + y)

=> 10y + x + 9 = 30x + 3y

=> 7y - 29x = -9 .......(2)

From equation (1) and (2)

we get,

=> Frome equation (1) we get,

=> x = 9 - y ........(3)

put the value of equation (3) in equation (2)

we get,

=> 7y - 29( 9 - y) = -9

=> 7y - 261 + 29y = -9

=> 36y = -9 + 261

=> 36y = 252

=> y = 7

put the value of y = 7 in equation (3)

we get,

=> x = 9 - 7

=> x = 2

Therefore,

original number = 10x + y

=> 10(2) + 7 = 27

Original number = 27.

Answer 2

Step-by-step explanation:

Assume that the ten's digit number be x and one's digit number be y.

The sum of the digits of a two-digit number is 9.

→ x + y = 9

→ x = 9 - y .............(1)

If 9 is added to the number formed by reversing the digits, then the result is thrice the original number.

• Original Number = 10x + y
• Reversed Number = 10y + x

As per given condition,

→ 10y + x + 9 = 3(10x + y)

→ 10y + x + 9 = 30x + 3y

→ 7y - 29x = - 9

→ 7y - 29(9 - y) = -9

→ 7y - 261 + 29y = - 9

→ 36y = 252

→ y = 7

Substitute value of y in (1)

→ x = 9 - 7

→ x = 2

Hence, the original number is 27.