MIXTURE AND ALLIGATION

Mixture and Alligation is a highly logical topic in CSAT that mainly tests proportional reasoning rather than calculation skills. Questions are generally framed around real-life situations such as mixing milk and water, alcohol and water, rice varieties, or solutions of different strengths. If the core concept is clear, this chapter becomes one of the easiest scoring areas in CSAT.

2. BASIC CONCEPT OF MIXTURE

Mixture
• A combination of two or more substances mixed together
• Components retain their individual properties

Examples
• Milk and water
• Alcohol and water
• Different qualities of rice or wheat

CSAT Assumption
• Mixing is uniform unless stated otherwise

3. MEANING OF ALLIGATION

Alligation
• A rule used to find the ratio in which two or more ingredients at different prices or strengths must be mixed to obtain a mixture of desired price or strength

Purpose
• To avoid lengthy calculations
• To directly find mixing ratio

4. ALLIGATION RULE (CORE CONCEPT)

Assume:
• Cheaper component = C
• Dearer component = D
• Mean value (mixture) = M

Rule
• Ratio of quantities = (D − M) : (M − C)

Important Logic
• Difference is taken diagonally
• Always subtract smaller from larger

Cheaper (C)      Dearer (D)
      \                 //
        Mean (M)

         /               \\

• Ratio = (D − M) : (M − C)

APPLICATION IN PRICE-BASED MIXTURES

Example Logic
• Rice at Rs. 20/kg mixed with rice at Rs. 40/kg to get mixture at Rs. 30/kg
• Ratio = (40 − 30):(30 − 20) = 10:10 = 1:1

7. APPLICATION IN PERCENTAGE / STRENGTH MIXTURES

Used in:
• Alcohol-water
• Acid solution
• Salt solution

Example Logic
• 20 percent solution mixed with 40 percent solution to get 30 percent
• Ratio = (40 − 30):(30 − 20) = 1:1

REPLACEMENT TYPE MIXTURE QUESTIONS (VERY IMPORTANT)

Concept
• A part of mixture is removed and replaced by another substance

Key Understanding
• Quantity removed contains both components in same ratio as mixture
• Replacement changes the concentration gradually

CSAT Tip
• Use ratio logic instead of formula

MULTIPLE REPLACEMENT CONCEPT

• Each replacement reduces original component proportionately
• Effect is multiplicative, not additive

Used in
• Repeated milk-water replacement questions

PRACTICE QUESTIONS 

Question 1
In what ratio should milk at Rs. 30 per litre be mixed with milk at Rs. 50 per litre so that the mixture costs Rs. 40 per litre?

Question 2
A vessel contains 40 litres of milk. 10 litres of milk is removed and replaced by water. This process is repeated once more. Find the quantity of milk left in the vessel.

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Subject: CSAT

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