A two-digit number is 7 times the sum of its two digits. Another number, formed by reversing its digits, is 18 less than the original number. Find the original number.

The original number is 42.

Let the number be 10a + b, equal to 7(a + b).

10a + b = 7a + 7b gives 3a = 6b, so a = 2b.

Reversal is 18 less: (10a + b) - (10b + a) = 18, so a - b = 2.

With a = 2b: 2b - b = 2, b = 2 and a = 4.

The number is 42.