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Question

The average marks of $$48$$ students in a class is $$45$$. The average marks of the boys in the class is $$40$$ and the average marks of the girls in the class is $$50$$. What is the ratio between the numbers of boys and the number of girls in the class?


A
2;1
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B
11:1
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C
1:1
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D
1:2
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Solution

The correct option is A $$1:1$$
Total marks of $$48$$ students $$= 48 x 45 = 2160$$
Let the number of boys be $$B$$ and the number of girls be $$(48 - B) $$
Then total marks of boys $$= 40B$$
Total marks of girls $$= 50 (48 - B) = 2400 - 50B$$
$$\displaystyle \Rightarrow$$ $$40B + 2400 - 50B = 2160$$ 
$$\displaystyle \Rightarrow$$ $$10B = 240 $$
$$\displaystyle \Rightarrow$$ $$B = 24$$
Thus number of girls $$= 48 - 24 = 24$$
Therefore, required ratio $$= 24 : 24 = 1 : 1$$

Mathematics

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