Math, asked by rashidsiddiqui7503, 10 months ago

A number consist of two digit whose sum is8. if 18is added to the number the digit are interchanged find the number

Answers

Answered by Sauron
29

Answer:

The Orignal Number is 35.

Step-by-step explanation:

Given :

Sum of digits = 8

The digits interchange when = 18 is added to the original number

To find :

The number

Solution :

\textsf{\underline{\underline{Original number -}}}

Let the digits be,

  • Units place as y
  • Tens place as 10(8 - y)

⇒ 10(8 - y) + y

⇒ 80 - 10y + y

80 - 9y --------- (Orignal Number)

\rule{300}{1.5}

\textsf{\underline{\underline{Number with reversed digits -}}}

Let the digits be,

  • Units place as (8 - y)
  • Tens place as 10(y)

⇒ 10(y) + (8 - y)

⇒ 10y + 8 - y

9y + 8 -------- (Number with reversed digits)

\rule{300}{1.5}

\textsf{\underline{\underline{According to the question - }}}

Number gets reversed when 18 is added.

⇒ (80 - 9y) + 18 = 9y + 8

⇒ 98 - 9y = 9y + 8

⇒ - 9y - 9y = 8 - 98

⇒ 18y = 90

⇒ y = 90/8

⇒ y = 5

\rule{300}{1.5}

\textsf{\underline{\underline{Original Number -}}}

⇒ 80 - 9y

⇒ 80 - 9(5)

⇒ 80 - 45

⇒ 35

\therefore The Orignal Number is 35.

Answered by VishalSharma01
93

Answer:

Step-by-step explanation:

Given :-

Sum of 2-digit number = 8

If 18 is added to the number, the digits change their places.

To Find :-

The Number

Solution :-

Let one of the number be x

And the other number be 8 - x

According to the question,

10x + (8 - x) + 18 = 10(8 - x) + x

⇒ 10x + 8 - x + 18 = 80 -10x + x

⇒ 9x + 26 = 80 - 9x

⇒ 9x + 9x = 80 - 26

⇒ 18x = 54

⇒ x = 54/18

x = 3

One Number = x = 3

Other number = 8 - x = 8 - 3 = 5

Hence, the number is 35.

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