Question

A number consists of two digits whose sum is 11 .if 27 is added to the number then the digits changes their places.what is the nymber?

Answer 1

Let the tenth digit be x and unit y.

Their sum ,

$\mathsf{x + y = 11 ------(1)}$

So, the number is

▶$\bold{ \mathsf{x \times 10 + y}}$

▶$\bold{ \mathsf{10 x + y}}$

When digits are interchanged,

the number is

▶$\bold{\mathsf{ y \times 10 + x}}$

▶$\bold{ \mathsf{10 y + x}}$

According to question,

If 27 is added the number gets interchanged.

▶$\bold{\mathsf{ (10 x + y) + 27 = 10 y + x}}$

▶ $\mathsf{ 10 x + y + 27 = 10 y + x}$

▶ $\mathsf{ 10 x - x -10y + y = -27}$

▶$\mathsf{ - 27 = 9x - 9y- - -(2)}$

On multiplying eq (1) by 9

$\mathsf{ (x + y = 11) \times 9}$

$\mathsf{ 9x + 9y = 99 ------(2)}$

On adding eq (2) by eq (1)

$\mathsf{ 9x + 9y = 99}$

$\mathsf{9x -9y = -27}$

_______________

$\mathsf{18x = 72}$

_______________

$\mathsf{x= \frac{72}{18}}$

$\huge \boxed{\mathsf{x \: = 4}}$

Since the sum of its digit is 11,

$\mathsf{4 + y= 11}$

$\mathsf{y= 11 - 4}$

$\huge \boxed{\mathsf{y \: = 7}}$

So, the number is,

▶$\bold{ \mathsf{4 \times 10 + 7}}$

NUMBER IS

$\huge \boxed{\boxed{\mathsf{47}}}$

Answer 2

Question :

A number consists of two digits whose sum is 11 .If 27 is added to the number then the digits changes their places.What is the number?

Answer : 47

Step by step explanation :

Let's assume that the digit in ten's place be x

Hence, we can say that

The digit in unit's place be (11-x)

Hence,

As per your question,

Number formed =  10x + ( 11 - x ) = 9x + 11

Therefore, As per next condition,

( 9x + 11 ) + 27 = 10( 11 - x ) + x

9x + 38 = 110 - 9x

9x + 9x = 110 - 38

18x = 72

x =  4

Hence,

The digit in ten's place is 4

The digit in unit's place = 11- x

= 11- 4

= 7

Therefore,

Ten's place = 4

Unit's place = 7

So, the number formed = 47

Required number => 47

_______________________