Question

11. 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,
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Answer 1

Let x be the unit digit number,

then ten's digit number = 11 - x     (∵ sum of the digits of 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

∴ the required two digit number = 110 - 9x = 110 - 9 × 9 = 110 - 81 = 29