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Linear Equations In One Variable

Question
CBSEENMA8002262
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The digits of a two digit number differ by 5. If the digits are interchanged and the resulting number is added to the original number, then we get 99. Find the original number.

Solution

Let the digit at unit place be 'x'.
∴                    The digit at the tens place = (x+5)

∴                                original number =10(x+5) + x
   
        With interchange of digits, the new number = 10x + (x + 5)
  
     Now, According to the condition, we have
             [original number] + [New number] = 99
or         [10(x + 5) + x] + [10x + (x + 5)] = 99
or         [10x + 50 +x] + [10x + x + 5] = 99
or                        11x + 50 + 11x + 5 = 99
or                                       22x + 55 = 99
    Transposing 55 to RHS, we have
                                                  22x = 99 - 55 = 44
    Dividing both sides by 22, we have
                                               x = 44 divided by22 = 2

∴                                              x = 2
i.e.                                Unit place digit = 2

∴                                 Tens place digit = 2 + 5 = 7
                            Thus the original number = 72.


                                               

Some More Questions From Linear Equations in One Variable Chapter

Solve the following equation:

x-2=7

Solve the following equation:

y + 3 = 10

Solve the following equation:

6 = z + 2

Solve the following equations:

x - 2 = 7

Solve the following equation:

6 = z + 2

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