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
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.