CAT 2023

Slot 3

QA

Question & Solution

Let the volume of mixture A be $200 \text{ml}$, which implies that the quantity of cocoa in the mixture is $120 \text{ml}$, and the quantity of sugar in the mixture is $80 \text{ml}$.

Similarly, let the volume of mixture B be $300 \text{ml}$, which implies the quantity of coffee is $210 \text{ml}$, and the quantity of sugar in the mixture is $90 \text{ml}$.

Now, we combine mixture A and B in the ratio of 2:3 (for every 200 ml of mixture A, we take 300 ml of mixture B).

Hence, the total volume of mixture C is:
$$ 200 \text{ml} + 300 \text{ml} = 500 \text{ml} $$ The total quantity of sugar in mixture C is:
$$ 80 \text{ml} + 90 \text{ml} = 170 \text{ml} $$

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Now, mixture C is mixed with an equal amount of milk to make a drink. Therefore, the total quantity of the final mixture is:
$$ 500 \text{ml} + 500 \text{ml} = 1000 \text{ml} $$ The quantity of sugar in the final mixture remains $170 \text{ml}$.

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Hence, the percentage of sugar in the final mixture is:
$$ \frac{170}{1000} \times 100 = 17% $$

Therefore, the correct option is A.