Question

The sum of the digits of a two digit number is 12 . If the new number is formed by reversing the digit is greater than the original number by 54 . find the original number.

Answer 1

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Hey there !!


→ Let the ten's digit of the original number be x.

→ And, the unit's digit be y.


▶Now,

A/Q,

=> x + y = 12................(1).


Original number = ( 10x + y ).

Number obtained on reversing the digit = ( 10y + x ).


=> 10x + y + 54 = 10y + x.

=> 10x - x + y - 10y = -54.

=> 9x - 9y = -54.

=> 9( x - y ) = -54.

=> x - y = -54/9.

=> x - y = -6................(2).

▶On substracting equation (1) and (2), we get

x + y = 12.
x - y = -6.
(-)..(+)...(+).
________

=> 2y = 18.

=> y = 18/2.

=> y = 9.

▶ Put the value of ‘y’ in equation (1).

=> x + 9 = 12.

=> x = 12 - 9.

=> x = 3.


Therefore, the original number = 10x + y.

= 10 × 3 + 9.

$\huge \boxed{ = 39. }$


✔✔ Hence, the original number is founded ✅ ✅.

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$\huge \bf{ \# \mathbb{B}e \mathbb{B}rainly.}$

Answer 2

Let the ten's digit of the original number be x.
and, the unit's digit be y.
x + y = 12................(1).

Original number = ( 10x + y ).
reversing the digit = ( 10y + x ).
=> 10x + y + 54 = 10y + x.

=> 10x - x + y - 10y = -54.

=> 9x - 9y = -54.

=> 9( x - y ) = -54.

=> x - y = -54/9.

=> x - y = -6................(2).
substracting equation (1) and (2), we get



=> 2y = 18.

=> y = 18/2.

=> y = 9.
y in equation (1).

=> x + 9 = 12.

=> x = 12 - 9.

=> x = 3.
original number = 10x + y.

= 10 × 3 + 9.

= 39.