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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 original number by 63. find the two digit number.
Asked by nehasingh1010 | 07 May, 2019, 09:15: PM
Let x be the unit digit number,
then ten's digit number = 11 - x     (since sum of the digits of a two-digit number is 11)

→ Two digit number (Original)= 10(11 - x) + x = 110 - 10x + x = 110 - 9x

The two digit number formed by interchanging the digits = 10x + (11 - x)
= 10x + 11 - x
= 9x + 11

According to the condition in the question, we get
9x + 11 - (110 - 9x) = 63
→ 18x = 99 + 63
→ 18x = 162
→     x = 9
Therefore the required two digit number = 110 - 9x = 110 - 9 × 9 = 110 - 81 = 29

Answered by Yasmeen Khan | 08 May, 2019, 09:42: AM

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