Question

a number consists of two digits the sum of the digits is 8 if digits are interchanged then the new number becomes 36 less and the orginal number find the number

Answer 1

Answer:

answer is 3.2

explanation is here

Step-by-step explanation:

let the one number be x ( i will solve this on variable X )

so here is equation we got.

10x + (8 - x)  + 8 = 10 ( 8-x ) + x

making of equation is very difficult. you have to practice it but solving them is very easy.

 

10x + (8 - x)  + 8 = 10 ( 8-x ) + x

taking every variable with at one side and number at one other side

so  10x + ( -x + 8 )  + 8 = 10 ( 8-x ) + x

Eliminate redundant parentheses  -

10x - x + 8 + 8 = 10 ( 8- x ) + x

10 x - x + 16 = 80 - 10x - x

10x - x + 10x + x = 80 - 16

20x = 64

x = 64 / 20

x = 3.2

Answer 2

Given : A number consists of two digits. The sum of the digits is 8. If digits are interchanged, then the new number becomes 36 less and the orginal number.

To Find : What is the number?

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❍ Let us assume, that the tens digit is 'y' and the ones digit is 'x'. Now,

❐ Original number :

➟ 10y + x

❐ When digits are interchanged :

➟ 10x + y

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$\bf \leadsto \: { \fbox{y + x = 8} - - - - - - \lgroup\sf{Equation \: No. \: 1} \rgroup }$

$\bf \leadsto \: { \fbox{(10y + x) - (10x + y) = 36} - - - - - - \lgroup\sf{Equation \: No. \: 2} \rgroup }$

From Equation No. 2, we get

$\tt{ \longmapsto \: y = \dfrac{36 + 9x}{9} }$

Substituting the value of y in Equation No. 1, we get

➺ $\sf{y + x = 8}$

➺ $\sf{ \dfrac{36 + 9x}{9} + x = 8}$

➺ $\sf{ \dfrac{36 + 9x + 9x}{9} = 8}$

➺ $\sf{ \dfrac{36 + 18x}{9} = 8}$

➺ $\sf{36 + 18x = 8 × 9}$

➺ $\sf{18x = 72 - 36}$

➺ $\sf{x = \cancel\dfrac{36}{18} }$

➺ $\sf{x = 2}$

Substituting the value of x in Equation No. 2, we get

➺ (10y + x) - (10x + y) = 36

➺ (10y + 2) - (10 × 2 + y) = 36

➺ (10y + 2) - (20 + y) = 36

➺ 9y - 18 = 36

➺ 9y = 36 + 18

➺ y = 54/9

➺ y = 6

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Therefore, the original number is :

➲ 10y + x

➲ (10 × 6) + 2

➲ 60 + 2

➲ 62