1.

The digit at ones place of a 2-digit number is four times the digit at tens place. Thethe given number.ined bynumber obtained by reversing the digits exceeds the given number by 54. Find​

Answer»

Given :-

  • The digit at ones place of a 2-digit number is four times the digit at TENS place. The the given number obtained by REVERSING the digits exceeds the given number by 54.

To FIND :-

  • Required numbers

Solution :-

Let the tens digit be x then ones digit be y

  • Original number = 10x + y

The digit at ones place of a 2-digit number is four times the digit at tens place.

→ y = 4x ---(i)

The the given number obtained by reversing the digits exceeds the given number by 54.

  • Reversed number = 10y + x

→ 10x + y + 54 = 10y + x

→ 10x - x + y - 10y = - 54

→ 9x - 9y = - 54

→ 9(x - y) = - 54

→ x - y = - 6 --(ii)

Put the value of y in equation (ii)

→ x - 4x = - 6

→ - 3x = - 6

→ x = 2

Substitute the value of x in equation (i)

→ y = 4x

→ y = 4 × 2

→ y = 8

Hence,

  • Tens digit = x = 2
  • Ones digit = y = 8

Therefore,

  • Original number = 10x + y = 28
  • Reversed number = 10y + x = 82


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