1.

6. The digit at the tens place of a two-digit number is four times that is the units place. If the digits reversed, the new number will be 54 less than the original number. Find the number​

Answer»

Given:-

  • Sum of digits of the TWO digits number is four times that in the UNIT's place.
  • If the digits are reversed the new number will be 54 LESS that the original number.

To FIND:-

  • Find the original number..?

Solutions:-

  • Let the digits at unit place be y.
  • Let the digits at ten's place be x.

Number = 10x + y

Sum of digits of the two digits number is four times that in the unit's place.

=> x + y = 4y

=> x = 4y - y

=> x = 3y ......(i).

If the digits are reversed the new number will be 54 less that the original number.

Number obtained by reversing the digits = 10y + x

Number obtained by reversing the digits = 10x + y - 54

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

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

=> 54 = 9x - 9y

=> 54 = 9(x - y)

=> 54/9 = x - y

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

Putting the value of x from Eq (i). in Eq (ii).

=> 6 = x - y

=> 6 = 3y - y

=> 6 = 2y

=> y = 6/2

=> y = 3

Putting the value of y in Eq (ii).

=> 6 = x - y

=> 6 = x - 3

=> -x = -6 - 3

=> -x = -9

=> x = 9

So, Number = 10x + y

=> 10(9) + 3

=> 90 + 3

=> 93

Hence, the original number is 93.


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