The ratio of the number of boys to that of the girls in a school is 3 : 2. If 20% of the boys and 25% of the girls are scholarship holders, find the percentage of those who are NOT scholarship holders.

Correct option is B

Given:

Ratio of boys to girls: 3:2

Percentage of boys who are scholarship holders: 20%.

Percentage of girls who are scholarship holders: 25%.

Formula Used:

$$\text{Percentage of non-scholarship holders} = 100\% - \text{Percentage of scholarship holders}.$$

$$\text{Weighted percentage} = \frac{\text{Boys' percentage contribution} + \text{Girls' percentage contribution}}{\text{Total ratio}}.$$​

Boys' percentage contribution = $$20\% \times \frac{\text{Boys' ratio}}{\text{Total ratio}}$$​ 

Girls' percentage contribution = $$25\% \times \frac{\text{Girls' ratio}}{\text{Total ratio}}.$$​

Solution:

Total ratio = 3 + 2 = 5

$$\text{Boys' contribution} = 20\% \times \frac{3}{5} = 12\%$$​​

$$\text{Girls' contribution} = 25\% \times \frac{2}{5} = 10\%$$​​

Total percentage of scholarship holders = 12% + 10% = 22%

Percentage of non-scholarship holders = 100% - 22% = 78%

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