CMAT 2019 Solved Question Paper

Let the number of men be 'm' and number of women be 'w' in the class.
Given Average score of men = 70
⇒ Total score of men number of men = 70
⇒ Total score of men = 70 × m
Also, Average score of women = 83
⇒ Total score of women number of women = 83
⇒ Total score of women = 83 × w
Given the class average = 76
⇒ (Total score of men + Total score of women) (number of men + number of women)
$\Rightarrow \frac{70\times \mathit{m}+83\times \mathit{w}}{\mathit{m}+\mathit{w}}=76$
Let the ratio of number of men to women $\frac{\mathit{m}}{\mathit{w}}=\mathit{k}$
$\Rightarrow 70\mathit{k}+83=76\mathit{k}+76$
$\Rightarrow 6\mathit{k}=7$
$\Rightarrow \mathit{k}=7:6$
Hence the ratio of men to women in the class is 7 : 6.