Question

a number consists of two digits whose sum is 9 if 27 is subtracted from the original number its digits are interchanged find the original number​

Answer 1

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Answer 2

Answer:

The Original Number is 63.

Step-by-step explanation:

Given :

Sum of the digits = 9

When 27 is subtracted from the original number = the digits get interchanged

To find :

The original number

Solution :

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

Let the Digits be -

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

⇒ 10(9 - y) + y

⇒ 90 - 10y + y

⇒ 90 - 9y ........ [Original Number]

$\rule{300}{1.5}$

$\textsf{\underline{\underline{Number with Reversed Digits :- }}}$

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]

$\rule{300}{1.5}$

$\textsf{\underline{\underline{According to the Question :- }}}$

When 27 is subtracted from the original number, the digits get interchanged.

⇒ (90 - 9y) - 27 = 9y + 9

⇒ 63 - 9y = 9y + 9

⇒ 9y + 9y = 63 - 9

⇒ 18y = 54

⇒ y = $\tt{\dfrac{54}{18}}$

⇒ y = 3

$\rule{300}{1.5}$

★ Value of 90 - 9y (Original Number)

⇒ 90 - 9(3)

⇒ 90 - 27

⇒ 63

⇒ Original Number = 63

$\therefore$ The Original Number is 63.

$\rule{300}{1.5}$

Verification :

As the original number is 63, the number with interchanged digits will be 36. Check whether the condition given in the question matches or not.

Condition - When 27 is subtracted from the original number, the digits get interchanged.

⇒ 63 - 27

⇒ 36

$\therefore$ The Original Number is 63.