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Mixtures and Alligations with Ratios

CAT 2023 Slot 3 · Quantitative Ability · Easy · Arithmetic

This is an easy Quantitative Ability question from the CAT 2023 Slot 3 paper. It tests Arithmetic. The full answer key and a step-by-step explanation are below — try it yourself first, then reveal the solution.

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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

  1. A.

    21

  2. B.

    24

  3. C.

    16

  4. D.

    17

Answer

D

Explanation

Proportion of sugar in mixture A = 23+2=25=40%\frac{2}{3+2} = \frac{2}{5} = 40\%. Proportion of sugar in mixture B = 37+3=310=30%\frac{3}{7+3} = \frac{3}{10} = 30\%.

Mixture C combines A and B in ratio 2:32 : 3: Sugar % in C=2(40%)+3(30%)2+3=80+905=1705=34%\text{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 1:11 : 1), so the percentage of sugar is halved: Sugar % in drink=34%2=17%\text{Sugar \% in drink} = \frac{34\%}{2} = 17\%

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