Question

The sum of the two digit number of a two-digit number is $13 the number obtained by interchanging the digits of a given number is 8 then number by 27 find the number

Answer 1

GIVEN:

• The sum of the two digit number of a two-digit number is 13.
• The number obtained by interchanging the digits of a given number is less then number by 27

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 the two digit number of a two-digit number is 13.

According to question:-

$\bf{\hookrightarrow x + y = 13...1) }$

CASE:- 2

The number obtained by interchanging the digits of a given number is less then number by 27.

• Number obtained by reversing the digits = 10y + x
• Number obtained by reversing the digits = 10x + y – 27

$\rm{\hookrightarrow 10y + x = 10x + y - 27}$

$\rm{\hookrightarrow 27 = 10x + y - 10y - x }$

$\rm{\hookrightarrow 27 = 9x - 9y}$

Divide by 9 on both sides

$\bf{\hookrightarrow 3 = x - y....2) }$

$\rm{\hookrightarrow x = 3 + y}$

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

$\rm{\hookrightarrow 3+y + y = 13 }$

$\rm{\hookrightarrow 2y = 13 - 3}$

$\rm{\hookrightarrow 2y = 10 }$

$\rm{\hookrightarrow y = \cancel\dfrac{10}{2}}$

$\bf{\hookrightarrow y = 5 }$

Put the value of 'y' in equation 1)

$\rm{\hookrightarrow x + 5 = 13 }$

$\rm{\hookrightarrow x = 13-5 }$

$\bf{\hookrightarrow x = 8 }$

• NUMBER = 10x + y
• NUMBER = 10(8) + 5
• NUMBER = 80 + 5
• NUMBER = 85

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