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Linear Equations In One Variable

Question
CBSEENMA8002276
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Sum of the digits of a two-digit number is 9. When we interchange the digits, it is found that the resulting new number is greater than the original number by 27. What is the two-digit number?

Solution

                Let the unit's digit = x

∴                      The ten's digit = (9-x)

∴                The original number = 10(9-x) + x
                                            = 90 - 10x + x
                                            = 90- 9x
   On interchanging the digits, the new number = 10x + (9 - x)
                                                             = 10x + 9 - x
                                                             = 9x + 9
 According to the condition, we have
                         [New number] = [Original number] + 27
or                                 9x + 9 = 90 - 9x + 27
or                                 9x + 9 = 117 - 9x
or                                        9x = 117 - 9 -9x      [Transposing 9 to RHS]
or                                   9x + 9x = 108                [Transposing (-9x) to LHS]
or                                        18x = 108
   Dividing both sides by 18, we have
                                         x equals 108 over 18 equals 6

∴               The original number = 90 - (9 cross times 6)
                                           = 90 - 54 = 36




 
 

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