Q14 of 46 Page 175

The sum of the digits of a two-digit 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.

Let, the unit’s digit = x


The ten’s digit = 12 – x


∴ The number = 10(12 – x) + x = 120 – 9x


After reversing,


Unit’s digit = 12 – x


Ten’s digit = x


∴The number after reversing = 10x + 12 – x = 9x + 12


According to problem,


⇒ 9x + 12 = 120 – 9x + 18


⇒ 18x = 126


⇒ x = 7


∴ The original number,


⇒ 120 – 9 × 7


⇒ 57


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