The sum of the digits of a two-digit number is 15. The number obtained by interchanging the digits exceeds the given number by 9. Find the number.

Step-by-step solution

Idea: Write the number as 10x + y and its reverse as 10y + x. Their difference is 9(y − x).

1. Tens digit x, units digit y: x + y = 15 … (1).½ mark
2. (10y + x) − (10x + y) = 9 ⇒ 9y − 9x = 9 ⇒ y − x = 1 … (2).1 mark
3. (1) + (2): 2y = 16 ⇒ y = 8, x = 7.1 mark
4. The number is 78.½ mark

Check: 87 − 78 = 9 ✓ and 7 + 8 = 15 ✓.

Answer to write in the exam

Common mistakes that cost marks

• Subtracting the wrong way and getting 87.
• Forgetting to divide 9y − 9x = 9 by 9.

How this can come in the exam

Try one yourself

The digits of a two-digit number add to 12, and the reversed number is 18 less than the number. Find it.

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