The strength of a salt solution is p% if 100 ml of the solution contains p grams of salt. If three salt solutions A, B, C are mixed in the proportion 1 : 2 : 3, then the resulting solution has strength 20%. If instead the proportion is 3 : 2 : 1, then the resulting solution has strength 30%. A fourt

Question

The strength of a salt solution is p% if 100 ml of the solution contains p grams of salt. If three salt solutions A, B, C are mixed in the proportion 1 : 2 : 3, then the resulting solution has strength 20%. If instead the proportion is 3 : 2 : 1, then the resulting solution has strength 30%. A fourth solution, D, is produced by mixing B and C in the ratio 2 : 7. The ratio of the strength of D to that of A is?

Accepted Answer

1 : 3 — Easy Let strengths of A, B, C be $a,b,c$. The two mixing ratios give two weighted-average equations. We don't need all three values — combine the equations to express $2b+7c$ (which appears in D's recipe) in terms of $a$. 1 Ratio $1:2:3$ gives strength $20\%$. $$\begin{aligned} &\frac{a+2b+3c}{1+2+3} = 20\ &\Rightarrow\ a+2b+3c = 120 \quad	ext{(1)} \end{aligned}$$ 2 Ratio $3:2:1$ gives strength $30\%$. $$\begin{aligned} &\frac{3a+2b+c}{3+2+1} = 30\ &\Rightarrow\ 3a+2b+c = 180 \quad	ext{(2)}

CAT 2018 Slot 2 — QA Question 10

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