Math, asked by swarupmanna2003, 9 months ago

The digit of a 2-digit number differ by 5. If the digits are interchanged and the resulting number is added to the original number, we get 99. Find the original number.​

Answers

Answered by VishnuPriya2801
12

Answer:-

Let the number be (10x + y).

Given:

Difference of the digits = 5

→ x - y = 5 -- equation (1).

And,

The Sum of the number and number formed by interchanging the digits = 99

→ 10x + y + 10y + x = 99

→ 11x + 11y = 99

→ 11(x + y) = 99

→ x + y = 99/11

→ x + y = 9 -- equation (2).

Adding equations (1) & (2) we get,

→ 2x = 14

→ x = 14/2

x = 7

Substitute "x" value in equation (1).

→ x - y = 5

→ 7 - y = 5

→ y = 7 - 5

y = 2

The number = 10x + y = 10(7) + 2 = 72.

Hence, the Original number is 72.

Answered by Anonymous
8

QUESTION :

The digit of a 2-digit number differ by 5. If the digits are interchanged and the resulting number is added to the original number, we get 99. Find the original number.

ANSWER :

Let the digit in ten's.Place be x and the digit in the ones place be y.

∴x + y = 5 ⟶( i )

∴Two digit number = 10x + y

Two digit after reversing the digits = 10y + x

According to the question,

∴10x + y + 10y + x = 99

⇒11 x + 11y = 99

⇒x + y = 99 ⟶( ii )

On adding equation i) and ii)

2x = 14

x = 14÷2

x = 7

Putting the value of x in equation i)

x - y = 5

⇒y = 2

∴Number = 10 y + x

= 72

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