Two numbers, m and n, are such that the sum of 4% of m and 6% of n is equal to half of the sum of 7% of m and 14% of n. Determine the ratio of m : n.

Correct option is C

Given:

4% of m + 6% of n = $$\frac{1}{2}$$​ of [7% of m + 14% of n]

Solution:

​$$\frac{4}{100}m + \frac{6}{100}n = \frac{1}{2} \left( \frac{7}{100}m + \frac{14}{100}n \right) \\ \ \\4m + 6n = \frac{1}{2}(7m + 14n) \\ \ \\8m + 12n = 7m + 14n \\ \ \\8m - 7m = 14n - 12n \\ \ \\m = 2n \\ \ \\\frac{m}{n} = \frac2 1$$​​

Thus, m : n = 2 : 1