Q. 11

# The sum of the digit

Let the digit in the ones place be x.
Then the digit in the tens place will be 12 – x.
Therefore, the original number = 10(12 - x) + x = 120 – 10x + x = 120 - 9x.
And, the new number = 10 x + (12 - x) = 10x + 12 – x = 9x + 12.
By the given condition,
New number = original number + 18
9x + 12 = 120 – 9x + 18
9x + 12 = 138 – 9x
9x + 9x = 138 – 12 (Transposing 9x and 12)
18x = 126
(Dividing both sides by 18)

x = 7
Thus, ones digit is 7 and tens digit is 12 - 7 = 5. Hence, the required number is 57.
Check: (1) 5 + 7 = 12 is the sum of the digit.
(2) New number = 75.
Difference between the original number and new number = 75 – 57 = 18.
\\\\ The new number is 18 more than the original number.

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