Question

The sum of the two digits of a number is 8. If the number is subtracted from the number obtained by reversing its digits, the result is 54. Find the number ?

Answer 1

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▶ Question - The sum of the two digits of a number is 8. If the number is subtracted from the number obtained by reversing its digits, the result is 54. Find the number.



▶ Explanation :-



Given sum of the two digits of a numbers is 8



Let the unit digit be y and tens digit be x



∴ x + y = 8 ------- ( 1 )



Let the number be 10x + y



Given the number is subtracted from the number obtained by reversing its digits, the result is 54



∴ Reversed number = 10y + x



According to the Question :-


=> 10y + x - ( 10x + y ) = 54


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


=> 9y - 9x = 54


=> 9 ( y - x ) = 54


=> y - x = 6


=> x - y = - 6


=> x = - 6 + y


Substituting value of x in equation ( 1 ) we get :-


=> x + y = 8


=> - 6 + y + y = 8


=> - 6 + 2y = 8


=> 2y = 8 + 6


=> 2y = 14


=> y = 14 / 2


=> y = 7


Substituting value of y in equation ( 1 ) we get :-


=> x + y = 8


=> x + 7 = 8


=> x = 8 - 7


=> x = 1


∴ Original Number = 10x + y


= 10 × 1 + 7


= 10 + 7


= 17


∴ Reversed number = 10y + x


= 10 × 7 + 1


= 70 + 1


= 71




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Answer 2

_________Heyy Buddy ❤________

______Here's your Answer ____________

Given;

sum of the two digits of a numbers is 8

Let the unit digit be y and tens digit be x

∴ x + y = 8 ------- ( 1 )

Let the number be 10x + y

Given;

The number is subtracted from the number obtained by reversing its digits, the result is 54

∴ Reversed number = 10y + x

A.T.Q.

=> 10y + x - ( 10x + y ) = 54

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

=> 9y - 9x = 54

=> 9 ( y - x ) = 54

=> y - x = 6

=> x - y = - 6

=> x = - 6 + y

Putting x = (-6 + y) in equation ( 1 ). we get,

=> x + y = 8

=> - 6 + y + y = 8

=> - 6 + 2y = 8

=> 2y = 8 + 6

=> 2y = 14

=> y = 14 / 2

=> y = 7

Putting y = 7 in equation (1) we get :-

=> x + y = 8

=> x + 7 = 8

=> x = 8 - 7

=> x = 1

∴ Original Number = 10x + y

= 10 × 1 + 7

= 10 + 7

= 17

∴ Reversed number = 10y + x

= 10 × 7 + 1

= 70 + 1

= 71.
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