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.

Solution / समाधान

According to the question:

$4% \text{ of } m + 6% \text{ of } n = \frac{1}{2}(7% \text{ of } m + 14% \text{ of } n)$

So,

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

Multiply both sides by 100:

$4m + 6n = \frac{1}{2}(7m + 14n)$

Multiply both sides by 2:

8m + 12n = 7m + 14n

8m - 7m = 14n - 12n

m = 2n

Therefore,

m : n = 2 : 1

Correct Answer / सही उत्तर:

2 : 1