Question

A number has two digits. the digit at tens Place is four times the digit at units place. If 54 is subtracted from the number, the digit are reversed. find the number.

Answer 1

Hi.

Good Question and Keep Progressing.

Here is your answer---

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Let the tens digit in two digit number be x and once digit be y.

Thus, Number = 10x + y

According to the Question,

 x = 4y -------------------------------eq(i)

Also,
    10x + y - 54 = 10y + x
     10x - x + y - 10y = 54
       9x  - 9y = 54
        9(x - y) = 54
     
     x - y = 6 ------------------------------eq(ii),

Putting eq(i) in eq(ii),

  x - y = 6
  4y - y = 6
    3y = 6
     y = 2

Putting y = 2 in eq(i),
   x = 4y
   x = 4 * 2
   x = 8

Thus, Number = 10x + y
                        = 10(8) + 2
                        = 80 + 2
                        = 82

Thus, the two-digit number is 82.

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Hope it helps.

Have a nice day.

Answer 2

• Thus, Number = 10x + y

According to the Question,

 x = 4y -------------------------------eq(i)

Also,

 

 10x + y - 54 = 10y + x

    10x - x + y - 10y = 54

      9x  - 9y = 54

       9(x - y) = 54

x - y = 6 ------------------------------eq(ii),

Putting eq(i) in eq(ii),

 x - y = 6

 4y - y= 6

   3y = 6

    y = 2

Putting y = 2 in eq(i),

  x = 4y

  x = 4 * 2

  x = 8

Thus, Number = 10x + y

                       = 10(8) + 2

                       = 80 + 2

                      = 82