Mixtures and concentration · 4 marks

Calculate the concentration of spice mix in these two scenarios.

(i) A 100 mL kashayam/kadha with 5% spice mix, a 200 mL one with 10% spice mix, and a 300 mL one with 15% spice mix are combined.
(ii) A 300 mL kashayam/kadha with 5% spice mix, a 200 mL one with 10% spice mix, and a 100 mL one with 15% spice mix are mixed.

Answer: (i) 7000600 ≈ 11.67% (ii) 5000600 ≈ 8.33%. Same three concentrations, but the answer moves towards whichever one comes in the largest quantity.

Step-by-step solution

Idea: Concentration of the mixture = total spice mixtotal kashayam = weighted mean of the percentages, with the volumes as weights.

(i) A 100 mL kashayam/kadha with 5% spice mix, a 200 mL one with 10% spice mix, and a 300 mL one with 15% spice mix are combined.

Spice mix = 100 × 5% + 200 × 10% + 300 × 15% = 5 + 20 + 45 = 70 mL.1 mark
Total volume = 100 + 200 + 300 = 600 mL. Concentration = 70600 × 100% ≈ 11.67%.1 mark

≈ 11.67% spice mix

(ii) A 300 mL kashayam/kadha with 5% spice mix, a 200 mL one with 10% spice mix, and a 100 mL one with 15% spice mix are mixed.

Spice mix = 300 × 5% + 200 × 10% + 100 × 15% = 15 + 20 + 15 = 50 mL.1 mark
Total volume = 600 mL. Concentration = 50600 × 100% ≈ 8.33%.1 mark

≈ 8.33% spice mix

(i) about 11.67% spice mix; (ii) about 8.33% spice mix. In (i) most of the kadha is the strong 15% one; in (ii) most is the mild 5% one.

Check: Both answers lie between 5% and 15%. (i) is above the middle value 10% and (ii) is below it by the same amount (1.67), because the volumes are simply reversed ✓.

Answer to write in the exam

(i)

Concentration = 100 × 5 + 200 × 10 + 300 × 15100 + 200 + 300 %

= 500 + 2000 + 4500600 % = 7000600 %

∴ Concentration ≈ 11.67%

(ii)

Concentration = 300 × 5 + 200 × 10 + 100 × 15300 + 200 + 100 %

= 1500 + 2000 + 1500600 % = 5000600 %

∴ Concentration ≈ 8.33%

Common mistakes that cost marks

Averaging 5%, 10% and 15% to get 10% for both scenarios. The volumes are different, so the answers differ.
Adding the percentages (30%) instead of finding the spice mix in each portion.
Dividing by 3 (portions) instead of the total volume 600 mL.

How this can come in the exam

Assertion–Reason (1 mark)

Assertion (A): Mixing 100 mL of a 5% solution with 300 mL of a 15% solution gives a concentration above 10%.
Reason (R): The concentration of a mixture is closer to that of the part with the larger quantity.

Both A and R are true, and R is the correct explanation of A.
Both A and R are true, but R is not the correct explanation of A.
A is true but R is false.
A is false but R is true.

Show answer

(A) Both A and R are true, and R is the correct explanation of A.
5 + 45400 = 12.5% > 10%. R is true and explains why A is true.

Try one yourself

200 mL of kadha with 6% spice mix is mixed with 300 mL with 16% spice mix. Find the concentration of the mixture.