Question

Anil mixes cocoa with sugar in the ratio 3 : 2 to prepare mixture A, and coffee with sugar in the ratio 7 : 3 to prepare mixture B. He combines mixtures A and B in the ratio 2 : 3 to make a new mixture C. If he mixes C with an equal amount of milk to make a drink, then the percentage of sugar in this drink will be

Accepted Answer

D. Proportion of sugar in mixture A = $\frac{2}{3+2} = \frac{2}{5} = 40\%$. Proportion of sugar in mixture B = $\frac{3}{7+3} = \frac{3}{10} = 30\%$. Mixture C combines A and B in ratio $2 : 3$: $$	ext{Sugar \% in C} = \frac{2(40\%) + 3(30\%)}{2 + 3} = \frac{80 + 90}{5} = \frac{170}{5} = 34\%$$ Mixture C is combined with an equal amount of milk (ratio $1 : 1$), so the percentage of sugar is halved: $$	ext{Sugar \% in drink} = \frac{34\%}{2} = 17\%$$

Mixtures and Alligations with Ratios

Explanation

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