Question:
Sum of the digits of a 2 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 2 digit number
Answer:
Let the unit place digit of a two-digit number be x
Therefore, the tens place digit = 9 - x
Now, 2-digit number = 10 * tens place digit + unit place digit
So, Original number = 10(9 - x) + x
According to the question, New number = Original number + 27
=> 10x + (9 - x) = 10(9 - x) + x + 27
=> 10x + 9 - x = 90 - 10x + x + 27
=> 9x + 9 = 90 - 9x + 27
=> 9x + 9 + 9x = 90 + 27
=> 18x + 9 = 117
=> 18x = 117 - 9
=> 18x = 108
=> x = 108/18
=> x = 6
Hence, the 2-digit number = 10(9 - x) + x
= 10(9 – 6) + 6
= 10 * 3 + 6
= 30 + 6
= 36
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