Multiple choice

The sum of digits of a two digit number is 16. If the number formed by reversing the digits is less than the original number by 18. Find the original number.

  1. 97

  2. 79

  3. 88

  4. 67

  5. 44
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A Correct answer
Explanation

Let unit digit be x, then tens digit = 16 - x. Therfore, original number = 10 *(16 - x ) + x = 160-9x. On reversing the digits, we have x at tens place and 16-x at unit place.Therefore, new number = 10x + 16 - x = 9x + 16. Original number-New number = 18 (160-9x)-(9x+16) = 18160 - 9x - 9x - 16 = 18 - 18x + 144 = 1818x = 144-1818x = 126x = 7. In the original number, we have at unit place tens digit = 16 - 7 = 9. Therefore, original number = 97. It is the correct answer.

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