Math, asked by knoxaryan9, 5 months ago

Sum of the digits of a two digit number is 11.When we interchange the digits, it is found
that the resulting new number is greater than the orginal number by 63. Find the two digit
number​

Answers

Answered by Arceus02
2

Given:-

  • Sum of original number = 11
  • On interchanging the digits, new number is formed
  • New number - original number = 63

To find:-

  • Original number

Answer:-

Original number:-

  • Let the unit's digit be x

Then the ten's digit will be (11 - x), such that unit's digit + ten's digit = x + 11 - x = 11 as given in the question.

Then, the value of the original number will be

(10 × Ten's digit) + (1 × Unit's digit)

→ [10 × (11 - x)] + (1 × x)

→ 110 - 10x + x

→ 110 - 9x ----( 1 )

New number:-

The new number is formed by interchanging the digits of the original number.

  • Unit's digit of new number = Ten's digit of original number = (11 - x)
  • Ten's digit of new number = Unit's digit of original number = x

Then the value of the new number will be

(10 × Ten's digit) + (1 × Unit's digit)

→ (10 × x) + [1 × (11 - x)]

→ 10x + 11 - x

→ 9x + 11 ----( 2 )

According to the question:-

New number - original number = 63

From ( 1 ) and ( 2 ),

→ (9x + 11) - (110x - 9x) = 63

→ 9x + 11 - 110 + 9x = 63

→ 18x - 99 = 63

→ 18x = 162

→ x = 162/18

→ x = 9 ---- ( 3 )

Putting this value of x in equation ( 1 ) to find the value of original number :-

Original number = 110 - 9x

→ Original number = 110 - (9 × 9)

→ Original number = 110 - 81

Original number = 29 Ans.

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