Math, asked by 15082008, 1 month ago

Sum of the digits of a two-digit number is 11. The given number is less than the

number obtained by interchanging the digits by 9.Find the number.​

Answers

Answered by AestheticSoul
4

Given :

  • Sum of the digits of a two digit number = 11
  • The given number is less than the number obtained by interchanging the digits by 9.

To find :

  • The number

Solution :

Let the two digit number be 10x + y.

where,

  • x and y are the two numbers

According to the first condition,

Sum of the digits of a two digit number :-

  • x + y = 11 ------(1)

Numbers obtained after interchanging the digits :-

→ 10y + x

According to the second condition,

The given number is less than the number obtained by interchanging the digits by 9.

→ 10x + y = 10y + x - 9

→ Grouping the like terms and solving them :

→ 10x - x = 10y - y - 9

→ 9x = 9y - 9

→ Taking 9 common from both the sides.

→ 9(x) = 9(y - 1)

→ 9 will get cancelled.

→ x = y - 1

x - y = - 1 ---------(2)

Solving equation 1 and 2 by using the method of making the coefficients same.

⠀⠀⠀⠀⠀⠀⠀⠀ x + y = 11

⠀⠀⠀⠀⠀⠀⠀⠀⠀x - y = - 1

⠀⠀⠀⠀⠀⠀ ━━━━━━━━

⠀⠀⠀⠀⠀⠀⠀⠀2x ⠀ = 10

⠀⠀⠀⠀⠀⠀ ━━━━━━━━

→ 2x = 10

→ Transposing 2 to the other side.

→ x = 10 ÷ 2

→ x = 5

The value of x = 5

Substituting the value of x in equation (1) :

→ x + y = 11

→ 5 + y = 11

→ y = 11 - 5

→ y = 6

The value of y = 6

Therefore,

  • The two numbers are 5 and 6.

And the two digit number is :-

→ 10x + y

→ 10(5) + 6

→ 50 + 6

→ 56

Therefore,

  • The two digit number = 56

━━━━━━━━━━━━━━━━━

Verification :

To verify the value of two digit number, substitute the value of x and y in the expression "10x + y = 10y + x - 9"

Taking LHS :

→ 10x + y

→ 10(5) + 6

→ 50 + 6

→ 56

LHS = 56

Taking RHS :

→ 10y + x - 9

→ 10(6) + 5 - 9

→ 60 + 5 - 9

→ 65 - 9

→ 56

RHS = 56

LHS = RHS

Hence, verified.

Answered by khushinaqvi15
1

Step-by-step explanation:

Let x be the unit digit of the number.

Then, the ten's digit = 11−x

Therefore, Number = 10(11−x)+x=110−10x+x=110−9x

When digits are interchanged ,

unit digit=11−x and tens digit =x

So, number obtained by interchanging the digits= 10x+(11−x)=9x+11

As per the question-

9x+11−(110−9x)=9

⇒9x+11−110+9x=9

⇒18x+11−110=9

⇒18x=9−11+110

⇒18x=108

⇒x=6

Hence, unit's digit = 6 and ten's digit = 11−6=5.

Therefore, the required number is 56. mark my answer as Brainallist

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