Question 55

In a class of 80 students, the ratio of the urban to the rural is 5 : 3. Ina test, the average score of the rural students is 40% more than that of the urban students. If the average score of all the students is 69, then what is the average score of the rural students ?

Solution

Total score of the class = $$69\times\ 80=5520$$

Let the average score of urban students be x then average score of rural students = $$\frac{140x}{100}=\frac{7x}{5}$$

Now,

$$50x+30\times\frac{7x}{5}==5520$$

$$92x=5520$$

$$x=\frac{5520}{92}=60$$

Hence, average score of rural students = $$60\times\frac{7}{5}=84\ $$.

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