Question

the sum of the digits of a 2- digit number is 9. if the number obtained by reversing the digits is 27 more than the original numbers, find the original number ​

Answer 1

$\bf{\huge{\underline{\boxed{\sf{\green{Answer:}}}}}}$

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

• The sum of the digits of a two digit number is 9.
• The number obtained by reversing the digits is 27 more than the original number

$\bf{\underline{\underline{\rm{\red{To\:find}}}}}$

• The original number

$\bf{\underline{\underline{\rm{\red{Solution:}}}}}$

Let the digit in the tens place be x

Let the digit in the units place be y

Original number = 10x + y

$\bf{\underline{\underline{\rm{\pink{As\:per\:the\:first\:condition:}}}}}$

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

Representing the condition mathematically,

=> x + y = 9 ----> 1

$\bf{\underline{\underline{\rm{\pink{As\:per\:the\:second\:condition:}}}}}$

• The number obtained by reversing the digits is 27 more than the original number

Reversed number = 10y + x

Representing the second condition mathematically,

=> 10y + x = 10x + y + 27

=> 10x + y + 27 = 10y + x

=> 10x - x + 27 = 10y - y

=> 9x + 27 = 9y

=> 9x - 9y = - 27

=> 9 ( x - y) = - 27

=> x - y = $\large\frac{-27}{9}$

=> x - y = - 3 ----> 2

Solve equations 1 and 2 simultaneously by elimination method.

Add equation 1 to equation 2,

x + y = + 9

x - y = - 3

----------------

2x = 6

=> x = $\large\frac{6}{2}$

=> x = 3

Substitute x = 3 in equation 1,

=> x + y = 9

=> 3 + y = 9

=> y = 9 - 3

=> y = 6

$\bf{\large{\underline{\boxed{\sf{\orange{Tens\:digit\:=\:x\:=\:3}}}}}}$

$\bf{\large{\underline{\boxed{\sf{\orange{Units\:digit\:=\:y\:=\:6}}}}}}$

$\bf{\large{\underline{\boxed{\sf{\orange{Original\:number\:=\:10x\:+\:y\:=\:10\:\times\:3\:+\:6=\:30\:+\:6\:=\:36}}}}}}$

Answer 2

Answer:

here your answer.........

36 [original number]

Step-by-step explanation:

let the tenth place digit be a

and unit place digit be b

then the number becomes 10a+b

According to question,

sum of the digits

a + b = 9

a + b - 9 = 0................... (1)

And

if the number obtained by reversing

the digits is 27 more than the

original numbers

10a + b + 27 = 10b + a

9a - 9b + 27 = 0

9 × [ a - b + 3 ] = 0

a - b + 3 = 0.......................(2)

now adding equations (1) + (2)

a + b - 9 + a - b + 3 = 0

2a - 6 = 0

2a = 6

a = 3

substitute 'a' in equation (1)

3 + b - 9 = 0

b - 6 = 0

b = 6

Required number:-

10a + b = 10 × 3 + 6 = 30 + 6 = 36.