Mixture & Alligation · Topic 4 of 6

🧪 Mixing Mixtures & Alloys

3 exam question types, fully solved

Here two ready-made mixtures (or two alloys) are poured together. The one rule to never break: you cannot average ratios directly — convert each to real amounts first.

Turn ratios into amounts, then add

For each vessel, split its quantity into the two components using its own ratio. Then add like-to-like — all the milk together, all the water together — and write the totals as a fresh ratio.

For two equal vessels, put both over a common denominator so the numerators add straight up: e.g. milk against water gives in one line.

• Alligation on strengths: the cross also works on percentages — to mix two solutions to a target strength, cross the two strengths around the target.

• Equal volumes blended ⇒ the final strength is just the average of the two strengths.

• Three-component price: use total cost total quantity mean, then solve for the unknown.

⚖️Alligation LabCross rule & replacement

Cheaper (c)

Dearer (d)

Mean (m)

Try a classic

cheaper : dearer=6 : 4=3 : 2

Mix 3 parts cheaper with 2 parts dearer

Distance intuition

m sits CLOSER to the cheaper (gap 4 vs 6) → the mix is mostly CHEAPER. Each ingredient's share is the distance to the OTHER value — the inverse-distance rule.

Equal vessels of milk : water and (over 4: milk , water ) combine to .

Q1Two equal vessels hold milk:water as 1:1 and 3:1. Mixed together, the ratio of milk to water is:

Q2Solutions that are 20% and 50% salt are mixed in the ratio 1:2. The salt percentage of the mix is:

Q3Two teas at ₹90/kg and ₹120/kg are mixed with a third in the ratio 1:1:2 to a mean of ₹150/kg. The third tea costs:

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Real exam questions — Mixing Mixtures & Alloys

3 question types · 9 solved examples from real SSC papers

Never average ratios — turn each mixture into real amounts, add component to component, then re-read the ratio. The cross also works straight on percentages.

How to solve this type

Never average the ratios directly — convert to actual amounts first. For each vessel, split its quantity into the two components using its own ratio. Then add component-to-component (all the milk, all the water) and write the totals as a fresh ratio. Using a fraction with a common denominator for equal vessels keeps the arithmetic clean.

Two vessels of equal capacity contain juice and water in the ratios 3 : 5 and 3 : 1. Both are poured into one vessel. Find the ratio of juice to water.

A13 : 9B9 : 7C8 : 9D7 : 3

Copper and gold are in the ratio 3 : 4 in the first alloy and 2 : 5 in the second. 14 kg of the first is mixed with 21 kg of the second. Find the ratio of copper to gold.

A23 : 12B17 : 13C5 : 9D12 : 23

Aluminium and zinc are in the ratios 5 : 6 and 3 : 5 in two alloys. 242 kg of the first and 144 kg of the second are mixed. Find the ratio of aluminium to zinc.

A76 : 117B82 : 111C93 : 100D68 : 125