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CAT 2023 Slot 3 — QA Question 13

MixturesEasy

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

Answer & solution

  • A

    21

  • 17

  • C

    16

  • D

    24

Solution

Easy

Pick concrete amounts of A and B in the given 2:32:3 ratio so the sub-ratios stay whole numbers. Add up the sugar from each, then dilute C with an equal mass of milk (which has no sugar) and read off the final sugar percentage.

Mixture A is cocoa:sugar =3:2=3:2, so sugar fraction =25=\tfrac{2}{5}. Mixture B is coffee:sugar =7:3=7:3, so sugar fraction =310=\tfrac{3}{10}. C is A:B =2:3=2:3. Take 2020 kg of A and 3030 kg of B.

1

Sugar contributed to C from A and from B:

from A=25×20=8 kgfrom B=310×30=9 kg⇒ sugar in C=8+9=17 kg in 50 kg of C\begin{aligned} &\text{from A}=\frac{2}{5}\times 20=8\ \text{kg}\\ &\text{from B}=\frac{3}{10}\times 30=9\ \text{kg}\\ &\Rightarrow\ \text{sugar in C}=8+9=17\ \text{kg in }50\text{ kg of C} \end{aligned}
2

Add equal milk (5050 kg, sugar-free) to make the drink, total 100100 kg, then find the sugar percentage:

1750+50×100%=17100×100%=17%\frac{17}{50+50}\times 100\%=\frac{17}{100}\times 100\%=17\%
Sugar in the drink=17%\text{Sugar in the drink}=\mathbf{17\%}

Choose 100100 kg of C from the start (i.e. 4040 kg A and 6060 kg B). Sugar =25(40)+310(60)=16+18=34=\tfrac{2}{5}(40)+\tfrac{3}{10}(60)=16+18=34 kg. Add 100100 kg milk →\to 3434 in 200200 =17%=17\%. Same answer, no fractions to chase.

CAT 2023 Slot 3 QA Q13: Anil mixes cocoa with sugar in the ratio 3 : 2 to prepare mixture A, and coffee with sugar in the ratio 7 : 3 — Solution | TheCATExam