Arithmetic

Mixture & Alligation

Easy

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

$17$

$24$

$16$

$21$

✅ Correct Option: 1

Mixture A: Cocoa and sugar in ratio 3:2

This means for every 3 parts cocoa, there are 2 parts sugar

Total parts = 3 + 2 = 5 parts

So in any amount of mixture A: cocoa = $\tfrac{3}{5}$ and sugar = $\tfrac{2}{5}$

Mixture B: Coffee and sugar in ratio 7:3

This means for every 7 parts coffee, there are 3 parts sugar

Total parts = 7 + 3 = 10 parts

So in any amount of mixture B: coffee = $\tfrac{7}{10}$ and sugar = $\tfrac{3}{10}$

Anil combines A and B in ratio 2:3. This means:

For every 2 units of A, he uses 3 units of B

Total mixture C = 2 + 3 = 5 units

Key insight: To make calculations easier, let's assume he takes 2 litres of A and 3 litres of B to make 5 litres of mixture C.

From 2 litres of mixture A:

Cocoa = $\tfrac{3}{5} \times 2 = 1.2$ litres

Sugar = $\tfrac{2}{5} \times 2 = 0.8$ litres

From 3 litres of mixture B:

Coffee = $\tfrac{7}{10} \times 3 = 2.1$ litres

Sugar = $\tfrac{3}{10} \times 3 = 0.9$ litres

Mixture C contains:

Cocoa: 1.2 litres

Coffee: 2.1 litres

Sugar: 0.8 + 0.9 = 1.7 litres

Total: 5 litres

Anil mixes C with an equal amount of milk.

Mixture C: 5 litres

Milk added: 5 litres

Final drink: 10 litres

In the final 10-litre drink:

Sugar content = 1.7 litres (only from mixture C, as milk contains no sugar)

Total volume = 10 litres

Percentage of sugar = $\tfrac{1.7}{10} \times 100\% = 17\%$

This approach works because ratios remain constant regardless of the actual quantities used. Whether we assume 2:3 litres or 20:30 litres for mixing A and B, the final percentage will always be the same.

The key is to convert ratios to fractions, use consistent units throughout, and remember that milk dilutes the mixture but doesn't add sugar.

Answer: 17%

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