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If 20% of (a+b) = 50% of (ab) and 40% of (a-b) = 70% of ab, then what fraction of a is b?

From \(0.2(a+b) = 0.5ab\) we get \(ab = 0.4(a+b)\). Substituting in \(0.4(a-b) = 0.7ab\) gives \(0.4(a-b) = 0.7 \times 0.4(a+b)\), so \(a-b = 0.7(a+b)\). This simplifies to…

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If 20% of (a+b) = 50% of (ab) and 40% of (a-b) = 70% of ab, then what fraction of a is b?

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Correct answer A

From 0.2(a+b)=0.5ab0.2(a+b) = 0.5ab we get ab=0.4(a+b)ab = 0.4(a+b). Substituting in 0.4(a−b)=0.7ab0.4(a-b) = 0.7ab gives 0.4(a−b)=0.7×0.4(a+b)0.4(a-b) = 0.7 \times 0.4(a+b), so a−b=0.7(a+b)a-b = 0.7(a+b). This simplifies to 0.3a=1.7b0.3a = 1.7b, hence ba=317\frac{b}{a} = \frac{3}{17}.

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