Average, Mixture & Alligation

Average, Mixture & Alligation

Concept

Average is simply the sum of values divided by the number of values. But SSC CGL doesn’t stop at basic averages — they test weighted averages where different groups have different sizes, replacement problems (removing and adding items), and the relationship between average and total sum. Mixture and Alligation is essentially a shortcut for solving weighted average problems visually. When you mix two items at different prices, the alligation method instantly gives the ratio without setting up equations.

The alligation method works because it equalises the deviations from the mean price. If one item is ₹10 above the mean and another is ₹10 below, mixing equal quantities brings the mean to exactly midway.

Key Points

• Average = Sum of observations / Number of observations.
• When one item replaces another in a group: New average = Old average ± (Change in total / Number of items).
• Alligation gives the ratio of quantities, not the actual amounts.
• If the mean is closer to one price, that ingredient dominates the mixture in higher proportion.
• For more than two ingredients, apply alligation successively — pair the lowest and highest first, then include the middle.

Worked Example

Q: The average weight of 30 students in a class is 48 kg. When 5 new students join, the average becomes 50 kg. Find the average weight of the new students. Approach: Total weight of original 30 = 30 × 48 = 1440 kg. Total weight of all 35 = 35 × 50 = 1750 kg. Weight of 5 new students = 1750 − 1440 = 310 kg. Average = 310 / 5 = 62 kg. Answer: 62 kg

SSC Pattern / Tips

• Replacement questions are common: when x items are removed and y items added, find the value of the removed/added items using total sum balance.
• For successive filling/emptying (tank problems), track the quantity of pure/liquid remaining each step.
• Alligation only works for two groups at a time — for 3+ groups, do it in steps.
• Average speed: harmonic mean approach for equal distances — not simple arithmetic mean.