Question

the sum of a two digits number is 9 if the the digits are reversed the nwe number exceeds the original the original number by 45 . find the original number​

Answer 1

Step-by-step explanation:

your answer is 27

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Answer 2

GIVEN:

• the sum of a two digits number is 9
• if the the digits are reversed the new number exceeds the original the original number by 45.

TO FIND:

• What is the original number ?

SOLUTION:

Let the digit at unit's place be 'y' and the digit at ten's place be 'x'

• Number = 10x + y

CASE:- 1

the sum of a two digits number is 9

$\bf{\hookrightarrow x + y = 9....1) }$

CASE:- 2

if the the digits are reversed the new number exceeds the original the original number by 45.

• Number obtained by reversing the digits = 10y + x
• Number obtained by reversing the digits = Original number + 45

According to question:-

$\rm{\hookrightarrow 10y + x = 10x + y + 45 }$

$\rm{\hookrightarrow -45 = 10x + y - 10y - x }$

$\rm{\hookrightarrow -45 = 9x - 9y}$

Divide by 9 on both sides

$\bf{\hookrightarrow -5 = x-y....2) }$

$\rm{\hookrightarrow y -5 = x}$

Put the value of 'x' from equation 2) in equation 1)

$\rm{\hookrightarrow y-5 + y = 9 }$

$\rm{\hookrightarrow 2y = 9+5 }$

$\rm{\hookrightarrow 2y = 14 }$

$\rm{\hookrightarrow y = \cancel\dfrac{14}{2}}$

$\bf{\hookrightarrow y = 7 }$

Put the value of 'y' in equation 1)

$\rm{\hookrightarrow x + 7 = 9 }$

$\rm{\hookrightarrow x = 9-7 }$

$\bf{\hookrightarrow x = 2 }$

• NUMBER = 10x + y
• NUMBER = 10(2) + 7
• NUMBER = 20 + 7
• NUMBER = 27

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