Question

the sum total two digits number is 12. the number formed by changing the digits is greater than the original number is 54. find the original number

Answer 1

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Answer 2

$\huge{\underline{\underline{\bf{GIVEN:-}}}}$

• the sum total two digits number is 12
• the number formed by changing the digits is greater than the original number is 54.

$\huge{\underline{\underline{\bf{TO\:FIND:-}}}}$

Find the original number = ?

$\huge{\underline{\underline{\bf{SOLUTION:-}}}}$

Let the digit in the unit's place be y and digit in the ten's place be x. Then,

∴ Number = 10x + y

∴ If the sum total two digits number is 12

According to given conditions:-

$\implies$$\large\bf\red{x + y = 12...1)}$

$\implies$$\bf{x = 12-y}$

Number obtained by reversing the digits = (10y + x)

∴ It is given that the digits interchange their place if 54 is added to the number

Number + 54 = Number obtained by interchanging the digits

$\implies$$\rm{10x + y + 54 = 10y + x}$

$\implies$$\rm{10x + y + 54 - 10y - x=0}$

$\implies$$\rm{9x - 9y = -54 }$

Divide by '9' on both sides

$\implies$$\large\rm\red{x - y = -6 ...2)}$

On putting the value of 'x' in equation 2), we get

$\implies$$\rm{(12-y) - y = -6}$

$\implies$$\rm{(12 - 2y = -6}$

$\implies$$\rm{ - 2y = -6 -12}$

$\implies$$\rm{ - 2y = -18}$

$\implies$$\rm{ y = \cancel\dfrac{18}{2}}$

$\implies$$\large\rm\red{ y = 9}$

Put the value of y in equation 1)

$\implies$$\bf{x + 9= 12}$

$\implies$$\bf{x = 12-9}$

$\implies$$\large\bf\red{x = 3}$

Number :-

$\implies$$\rm{10 \times 3 + 9}$

$\implies$$\large\rm{39}$

$\large{\underline{\underline{\bf{FINAL\:ANSWER:-}}}}$

$\huge{\boxed{\boxed{\bf{\red{NUMBER = 39}}}}}$