Alligation Method Shortcut Tricks with Examples

Last updated: June 27, 2026. For coaching and doubts, contactShortcut Maths, Jadavpur, Kolkata 700032. Call+91-9804490328.

The Visual "X" Cross Method

When two groups with values A and B are mixed to give a mean value M, the ratio of quantities is:

Ratio = (B − M) : (M − A)

Example 1: Mixtures

Question: Rice at ₹40/kg is mixed with rice at ₹60/kg to sell the mixture at ₹50/kg. Find the mixing ratio.

Example 2: Averages

Question: The average age of 20 boys is 14 years and of 30 girls is 16 years. Find the combined average.

Using weighted average: (20×14 + 30×16) ÷ 50 = (280 + 480) ÷ 50 = 760 ÷ 50 = 15.2 years.

Using alligation ratio 20:30 = 2:3 and values 14, 16, we get mean = 14 + (3/5)×2 = 15.2 years.

Example 3: Profit & Loss

Question: Two articles are sold at the same price. One gives 20% profit, the other 10% loss. What is the overall profit/loss percentage?

Assume selling price = ₹100 each. CP of first = 100/1.20 = ₹83.33 CP of second = 100/0.90 = ₹111.11 Total CP = ₹194.44, Total SP = ₹200 Profit % = (5.56/194.44)×100 ≈ 2.86% profit.

Alligation shortcut (SP same): overall ratio 1:1, profit/loss values +20 and −10. Mean = (20 − 10)/2 = +5% on SP basis, but converting to CP basis gives ≈ 2.86% profit.

Example 4: Simple Interest

Question: Two equal sums are lent at 8% and 12% simple interest. The average rate of interest is 10%. Find the ratio of sums.

Shortcut Maths Arithmetic batch covers percentages, profit-loss, SI/CI, time-work and mixtures using visual methods.

Learn Alligation + 50 More Shortcuts Shortcut Maths Arithmetic batch covers percentages, profit-loss, SI/CI, time-work and mixtures using visual methods. Join Batch Call 9804490328

FAQs

Direct alligation works for two groups. For three or more, use weighted average or apply alligation step-by-step.

It represents the ratio of quantities (by weight, volume or amount) of the cheaper and dearer components.

Yes, usually as 1-2 questions under arithmetic or DI sections. In Mains it appears in data interpretation sets.

Last updated: June 27, 2026. For coaching in Kolkata, call +91-9804490328.

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