Students in a commerce class took a test. The average score of men is 70 and of women is 83. The class average is 76. What is the ratio of men to women in the class?

Let the number of men be 'm' and number of women be 'w' in the class.

Given Average score of men = 70

$$\Rightarrow$$ Total score of men$$\div$$number of men = 70

$$\Rightarrow$$ Total score of men = 70$$\times$$m

Also, Average score of women = 83

$$\Rightarrow$$ Total score of women$$\div$$number of women = 83

$$\Rightarrow$$ Total score of women = 83$$\times$$w

Given the class average = 76

$$\Rightarrow$$ (Total score of men + Total score of women)$$\div$$(number of men + number of women) = 76

$$\Rightarrow \frac{70\times m + 83\times w}{m + w} = 76 $$

Let the ratio of number of men to women $$\frac{m}{w} = k$$

$$\Rightarrow$$ 70k + 83 = 76k + 76

$$\Rightarrow$$ 6k = 7 

$$\Rightarrow$$ k = 7 : 6.

Hence the ratio of men to women in the class is 7 : 6.