In a class, ratio of the boys to the girls is 5:3. If 20% of the boys and 40% of the girls fail an exam, what is the ratio of the number of boys who passed to the number of girls who passed?
20:9
Given: boys : girls = 5 : 3, with 20% of boys and 40% of girls failing.
Let boys \(=5k\) and girls \(=3k\) for some positive number \(k\).
Boys who passed \(=(100-20)\%=80\%\) of boys \(=0.8\times 5k=4k\).
Girls who passed \(=(100-40)\%=60\%\) of girls \(=0.6\times 3k=1.8k\).
Required ratio \(=\dfrac{4k}{1.8k}=\dfrac{4}{1.8}\).
Multiply numerator and denominator by 5: \(\dfrac{4\times 5}{1.8\times 5}=\dfrac{20}{9}\).
Hence the ratio of passed boys to passed girls is 20:9.
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