The ratio of a two-digit natural number to a number formed by reversing its…

Let the two-digit number be 10a + b and its reversed number be 10b + a.

Given (10a + b) / (10b + a) = 4/7. Cross-multiply and simplify:

• 7(10a + b) = 4(10b + a) ⇒ 70a + 7b = 40b + 4a ⇒ 66a = 33b ⇒ b = 2a.

Since a and b are digits (a = 1..9, b = 0..9) and b = 2a, the possible digit pairs are:

• a = 1, b = 2 ⇒ numbers 12 and 21

• a = 2, b = 4 ⇒ numbers 24 and 42

• a = 3, b = 6 ⇒ numbers 36 and 63

• a = 4, b = 8 ⇒ numbers 48 and 84

Sum all numbers from these pairs:

• 12 + 21 + 24 + 42 + 36 + 63 + 48 + 84 = 330

Answer: 330