Question

The sum of the digits of a two digits number is 12. If the new number formed by reversing the digits is greater than the original number by 18, find the original number. Check your solution.​

Answer 1

$\huge\underline\mathrm{SOLUTION:-}$

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 = 10x + (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

➠ $\mathsf {\frac{18x}{18} = \frac{126}{18} }$ (Divide both sides by 18)

➠ x = 7

Thus:

Ones digit is 7 and tens digit is 12 - 7 = 5.

• Hence, the required number is 57.

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