Average and Mixture Tricks for Bank and SSC Exams with Solved Questions

Quick answer: Average and mixture questions become fast when you convert them into totals or alligation. Use average × quantity for total value, compare deviations from the target average, and apply ratio shortcuts only after identifying both values correctly.

• Average shortcut: total = average × number of items.
• Mixture shortcut: use alligation when two values combine to one mean value.
• Common trap: percentage, price, weight and quantity must use the same unit before solving.

Average and alligation questions are quick marks if you use the deviation method instead of adding everything. Here are the shortcuts and practice questions.

Average shortcuts

• Average of an AP = (first + last)/2; average of 1 to n = (n + 1)/2
• Average of consecutive even/odd numbers = middle number
• Deviation method: assume an average, sum the deviations, divide by count
• New member raises average by x → new member = old average + (n + 1)x
• Member replaced and average changes by x → new − old member = nx
• Average speed for equal distances = 2ab/(a + b)

Alligation

Cheaper : dearer = (dearer price − mean price) : (mean price − cheaper price). Works for prices, percentages, speeds — anything averaged by quantity.

Solved questions

1. Average of 5 numbers is 20; one number 30 removed → new average 17.5
2. Average age of 30 students is 15; teacher included → 15.5 → teacher’s age 30.5
3. Average of first 50 natural numbers = 25.5
4. A cricketer’s average after 10 innings is 40; scores 62 in 11th → 42
5. Average of 8 numbers is 25; one number misread as 35 instead of 53 → correct average 27.25
6. Average speed going at 60 and returning at 40 = 48 km/h
7. Mixing 40% and 60% solutions to get 55% → ratio 1 : 3
8. Wheat at ₹24 and ₹30 mixed for ₹26 mean → 2 : 1
9. Average weight rises by 2 kg when 50 kg person replaced by X in group of 10 → X = 70
10. Average of 3 numbers is 20; the first two average 15 → third = 30
11. A class of 20 boys average 50, 30 girls average 60 → class average 56
12. Sum of 10 numbers 250; average of first 4 is 20 → average of the rest 28.3
13. Milk at ₹40 mixed with water to sell at ₹32 → water : milk = 1 : 4
14. Average marks 72 in 5 subjects; average of 4 is 70 → 5th = 80
15. Average of 11 numbers is 30; first 6 average 28, last 6 average 33 → 6th number = 36

Common mistakes

• Adding all numbers instead of using deviations
• Putting prices in the wrong order in alligation
• Using arithmetic mean for average speed with equal distances

Related: Ratio and proportion tricks.

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Frequently asked questions

Which exams is this Average and Mixture Tricks guide useful for?

SSC CGL, CHSL, MTS, GD, RRB NTPC and Group D, IBPS and SBI PO/Clerk, state PSC and other exams with a similar syllabus.

How much practice is needed for Average and Mixture Tricks?

Solve 20–30 questions daily for one to two weeks with a timer. Track the time per question and your accuracy; move on once accuracy is above 90 percent.

Can I get average tricks questions explained in Hindi?

Yes. DoubtPay AI explains any question in Hindi, Hinglish, English and nine other Indian languages, with step-by-step working. Packs start at ₹9 for 15 answers.