Mixture and Allegation for SSC CPO | Concepts & Practice

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Summary Formula Tricks Mistakes Solved Example Practice FAQ

Mixture and Allegation revision for SSC CPO: understand the base rule, apply the correct formula or relation, check common traps, then practise with approved questions.

Mixture and Alligation questions compare quantities or prices of components to obtain a required mean value. Alligation gives the ratio directly when two component values and the mean are known.

SSC CPO focus: Solve the core method first, then use the approved practice questions on this page to build exam-speed accuracy.

Mixture and Allegation revision rule: concept → formula/relation → one worked example → timed practice → error review.

Core concept
Key formula/relation
Common trap
Approved practice

Cheaper : Dearer = (Dearer-Mean) : (Mean-Cheaper)
Weighted mean = total value / total quantity

The required mean must lie between the two component values. If it does not, recheck the interpretation.

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Read the exact requirement before choosing a shortcut.
Keep units, signs and percentage bases consistent.
Use the final few seconds to verify direction and magnitude.

Using a memorised shortcut without checking its condition.
Skipping unit or base conversion.
Doing long arithmetic before identifying the underlying relation.

Practice example: Rice costing Rs. 40 per kg is mixed with rice costing Rs. 55 per kg to obtain a mixture worth Rs. 49 per kg. In what ratio should the cheaper and dearer rice be mixed?

Solution: The required ratio is 2:3.

Tea worth Rs. 60 per kg is mixed with tea worth Rs. 84 per kg to obtain a mixture worth Rs. 69 per kg. In what ratio are the cheaper and dearer varieties mixed?
Coffee worth Rs. 72 per kg is mixed with coffee worth Rs. 96 per kg to obtain a mixture worth Rs. 81 per kg. In what ratio are the cheaper and dearer varieties mixed?
In a Mixture and Allegation practice set, a student answers 18 questions correctly out of 24. What percentage is correct?

Learn the shortcut first

Shortcut before you solve

Mixture questions become short once you move from long equations to the alligation cross method.

Faster solving steps

Use this 4-step method before solving to keep your thinking fast and repeatable.

Step 1 Identify relation

Spot the pattern, relationship, or core idea first.

Step 2 Apply same pattern

Use the same rule instead of re-solving from scratch.

Step 3 Eliminate wrong options

Remove confusing choices before comparing the last few.

Step 4 Confirm final answer

Pick the option that matches the shortcut most cleanly.

Practice Questions

Start with the first 10 questions free, then unlock the rest with premium

Now apply the trick on real questions

Use the shortcut above before solving these questions

Use alligation when two values are mixed to get a mean value.

Tip: The ratio is found by cross-subtracting the mean from the two component values.

Step 1

Cross subtract: 30 - 26 = 4 and 26 - 20 = 6.

Step 2

Required ratio = 4 : 6 = 2 : 3.

Rule

Cheaper : dearer = (dearer - mean) : (mean - cheaper).

3-second trick

Write high price, mean price, low price, then cross subtract immediately.

Trap to avoid

Reversing the ratio after cross subtraction.

Correct answer

2 : 3

Thinking path

Take the higher and lower prices.
Subtract the mean crosswise.
Reduce the ratio if possible.

Final answer: 2 : 3

Why this is fast: Alligation avoids long linear equations in standard mixture problems.

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Q1 Medium

Coffee worth Rs. 72 per kg is mixed with coffee worth Rs. 96 per kg to obtain a mixture worth Rs. 81 per kg. In what ratio are the cheaper and dearer…