Question

The sum of the digit of a two digit number is 9 the number obtained by interchanging the digits is 27 less than the original number find the original number. ​

Answer 1

Let unit digit be X

Let tenth digit be y

Number = X +10y

A/q

X+y= 9

10x + y = X +10y+ 27

9x - 9y = 27

X - y = 3

X+y = 9

X -y=3

2x = 12

X = 12/2 = 6

6 + y= 9

Y= 9 -6 = 3

Number = 36

Answer 2

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

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

• The sum of the digit of a two digit number is 9
• The number obtained by interchanging the digits is 27 less than the original number

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

• The original number.

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

Let the digit in the tens place be x

Let the digit in the units place be y

Original two digit number = 10x + y

As per first condition :-

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

Representing it mathematically we get our first equation,

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

As per second condition :-

• the number obtained by interchanging the digits is 27 less than the original number

Number on interchanging the digit 10y + x

Interchanged number is 27 less than the original number.

Let's represent it mathematically.

10x + y = 10y + x - 27

10x - x = 10y - y - 27

9x = 9y - 27

9x - 9y = - 27

9 ( x - y) = - 27

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

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

Add equation 1 to 2,

x + y = 9 ----> 1

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

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

2x = 6

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

x = 3

Substitute x = 3 in equation 1,

x + y = 9 ----> 1

3 + y = 9

y = 9 - 3

y = 6

•°•Original Number = 10x + y

Original number = 10 × 3 + 6

Original number = 30 + 6

Original number = 36