Mixture & Alligation · Topic 3 of 6

💧 Changing Concentration

3 exam question types, fully solved

“How much water must be added to change the ratio?” is the single most common mixture question. It looks fiddly but cracks instantly once you spot the fixed component.

Anchor on the fixed component

When you add only ONE ingredient, the OTHER ingredient's quantity never changes. That fixed amount is your anchor — pin it down first, then everything else follows.

1. Split the starting mixture into its two amounts using the ratio.

2. The component you are NOT adding stays the same — find its litres.

3. See how many parts it is in the NEW ratio, get the value of one part, and read off the new total of the added ingredient. Subtract the old amount.

• For a target percentage, use the constant-product rule on the component that is NOT being added (its litres stay fixed while its drops).

⚖️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.

A 40 L mix is milk : water (milk 30, water 10). To make it , milk stays 30 = 3 parts, so water must be 2 parts = 20: add L.

Q1A 60-litre mixture of milk and water is in the ratio 3:1. How much water is added to make it 3:2?

Q2A 50-litre solution is 40% acid. How much water must be added to make it 25% acid?

Q3In an 80-litre mix, juice is 60 L and water 20 L. How much juice is added to make juice:water = 5:1?

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Real exam questions — Changing Concentration

3 question types · 9 solved examples from real SSC papers

When you add just one ingredient, the OTHER one never changes. Anchor on that fixed component and every “add water to change the ratio” question falls apart.

How to solve this type

The big idea: when you add only ONE ingredient, the OTHER ingredient’s quantity never changes — it is the anchor. Find that fixed quantity, decide how many “parts” it equals in the new ratio, get the value of one part, then read off the new total of the ingredient you added. Subtract its old amount to find how much was poured in. Always pin down the constant component first.

In a 55-litre mixture, fruit juice and water are in the ratio 4 : 1. How much water must be added to make the ratio 2 : 1?

A9B22C11D12

A 40-litre mixture of milk and water is in the ratio 7 : 3. How much water must be added so the mixture is 60% water?

A30B35C20D25

In a 60-litre mixture, milk and water are in the ratio 2 : 3. How much water must be added to make the ratio 1 : 2?

A56 litresB60 litresC76 litresD12 litres