Question

6. The sum of the digits of a two digit number is 9. The number obtained by reversing the digits is 9 less than the original number. find the number.


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Answer 1

Let the digits of the no. be x & y

x+y=9.............(1)

10x+y-9=10y+x.......... (2)

From (2) we get 9x-9y=9

So x-y=1.......... (3)

From (1) and (3)

2x=10

x=5

So y=4

Hence the no. is 54

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Answer 2

Answer:

The Orignal Number is 54.

Step-by-step explanation:

Given :

Sum of digits = 9

Number obtained by reversing the digits = 9 less than the original number

To Find :

The Orignal Number

Solution :

Orignal Number,

Let the digits be -

• Units as y
• Tens = 10(9 - y)

⇒ 10(9 - y) + y

⇒ 90 - 10y + y

⇒ 90 - 9y ------ (Orignal Number)

$\rule{300}{1.5}$

Number with reversed digits,

Let the digits be -

• Units place as (9 - y)
• Tens place as 10(y)

⇒ 10(y) + (9 - y)

⇒ 10y + 9 - y

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

$\rule{300}{1.5}$

According to the question,

Number with reversed digits is 9 less than the original number.

⇒ 90 - 9y = (9y + 9) + 9

⇒ 90 - 9y = 9y + 18

⇒ 90 - 18 = 9y + 9y

⇒ 72 = 18y

⇒ y = 72/18

⇒ y = 4

$\rule{300}{1.5}$

Orignal Number,

⇒ 90 - 9y

⇒ 90 - 36

⇒ 54

Original number is 54

Therefore, the Orignal Number is 54.