Scholarship 3

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

Correct answer:

p =  78 %

Step-by-step explanation:

$$\begin{gathered} b:g=3:2=3x:2x \\ {r}_1=20\%=\frac{20}{100}=\frac{1}{5}=0.2 \\ {r}_2=25\%=\frac{25}{100}=\frac{1}{4}=0.25 \\ s=r_1\cdot 3x+r_2\cdot 2x=x\cdot (3r_1+2r_2) \\ n=5x \\ r=\frac{n-s}{n}=\frac{5x-x\cdot (3r_1+2r_2)}{5x} \\ r=\frac{5-3\cdot r_1-2\cdot r_2}{5}=\frac{5-3\cdot 0.2-2\cdot 0.25}{5}=\frac{39}{50}=0.78 \\ p=100\cdot r=100\cdot 0.78=78\% \end{gathered}$$

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