20 Ultra-Fast Mixture Tricks (Must Know for Exams)

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২০টা Ultra-Fast Mixture Tricks (পৰীক্ষাৰ বাবে অতি জৰুৰী)

SSC, Railway, Banking, NDA, Olympiad আদি প্ৰতিযোগিতামূলক পৰীক্ষাত বহুত সহায় কৰে।

১. Allegation Rule (সবচেয়ে গুৰুত্বপূর্ণ)

দুটা ভিন্ন দাম বা শক্তিৰ বস্তু মিহলাই গড় মান পাবলৈ ব্যৱহাৰ কৰা হয়।

সূত্ৰ:

Ratio = (Dearer − Mean) : (Mean − Cheaper)
সদায় Cross subtraction কৰিব।

২. Replace Method Shortcut

যদি কিছুমান liquid উলিয়াই পানী দিয়া হয়:

সূত্ৰ:  Final = Original × (1− removed / total)ⁿ (n = কিমানবাৰ replace কৰা হৈছে)

৩. কেৱল পানী যোগ কৰিলে

Milk একেই থাকে।

Extra Water = (Milk × New Ratio) − Old Water

৪. কেৱল Milk যোগ কৰিলে

Water একেই থাকে।

Extra Milk = (Water ÷ New Ratio) − Old Milk

৫. একে পৰিমাণ বাৰে বাৰে উলিয়ালে

Remaining = V(1- r )ⁿ 

Exam-ত বহুত সোধে।

৬. Final Ratio সোনকালে উলিয়াবলৈ

Liter গণনা নকৰিব।

Ratio → Fraction লৈ তুলনা কৰক।

৭. Ratio Matching Trick 

যিটো quantity সলনি নহয়, প্ৰথমে তাক match কৰক।

Time 50% কমে।

৮. Weighted Average Trick

Mean = Total Quantity/Total Items ​-ত বহুত ব্যৱহাৰ হয়।

৯. Assumption Trick

মুঠ mixture LCM বা 100 ধৰি লওক।

Fraction এৰাই যাব পাৰিব।

১০. Percentage Conversion Trick

 

 

 Mental calculation সহজ হয়।

১১. Ratio সৰু হলে

পানী বাঢ়িছে বা milk কমিছে।

১২. Ratio ডাঙৰ হলে

Milk বাঢ়িছে বা পানী কমিছে।

 Logical check!

১৩. Successive Replacement Shortcut

আধা দুবাৰ replace কৰিলে:

Remaining=(1/2)2=1/4Remaining = (1/2)^2 = 1/4Remaining=(1/2)2=1/4

Long calculation নাই।

১৪. 100 ধৰা Method

37% যেনেকুৱা কঠিন percentage দেখিলে → Total = 100 L ধৰি লওক।

১৫. Difference Trick

Strength 40% → 25%

Decrease = 15%

মানে পানী = 15% of total

১৬. Cross Multiplication Trick

For ratio change: Old Milk / Old Total = New Milk / New Total

Solve in ONE step.

১৭. Exam Favourite Pattern

x liter উলিয়াই পানী দিলে purity বিচাৰিলে:

Remove x liters, add water → find purity.

Immediately use:

Pure left = Original(1- x / Total)

১৮. Extreme Shortcut

সদায় pure quantity track কৰক।

Examiner ইয়াক লুকুৱাই ৰাখে!

১৯. LCM Mega Trick

7:13 দেখা গেলে → Total = 20 বা 200 ধৰি লওক।

Decimal এৰাই যাব।

২০. Golden Rule of Mixture

দুয়োটা liquid track নকৰিব।
কেৱল যিটো unchanged তাক track কৰক।

Mixture chapter একেবাৰে সহজ হৈ যাব।

1. Allegation Rule

Used when two ingredients are mixed at different prices or strengths.

Formula: Ratio = (Dearer − Mean) : (Mean − Cheaper) Always subtract diagonally.

Ex : Mix ₹20 and ₹30 to get ₹25.

1st:
Cheaper = 20
Dearer = 30
Mean = 25

2nd: Cross Difference

30 - 25 = 5
25 - 20 = 5

3rd: Ratio

5 : 5 = 1 : 1

Equal quantities should be mixed.

Ultra-Fast Exam Trick

If the mean is exactly in the middle, the ratio is always 1 : 1.

Example:
10 & 20 → Mean 15
40 & 60 → Mean 50

No calculation needed!

2. Replace Method Shortcut

If liquid is removed and replaced with water:

Formula: Remaining liquid after n operations:

                 Final = Original × (1− removed / total)ⁿ

3. When Only Water is Added

Milk stays constant.

Extra Water = (Milk × New Water Ratio) − Old Water

4. When Only Milk is Added

Water stays constant.

Extra Milk = (Water ÷ New Ratio) − Old Milk

5. Equal Quantity Removed Repeatedly

Remember the power formula:

Remaining = V(1- r )ⁿ 

6. Find Final Ratio Quickly

Instead of calculating liters:

Convert ratios into fractions.

Exa:
3:2 → Milk = 3/5
1:2 → Milk = 1/3

Compare directly.

7. Ratio Matching Trick 

Always make the unchanged quantity equal.

Ex: Milk unchanged → match milk first, then adjust water.

Saves 50% time.

8. Weighted Average Trick

Used in concentration problems.

               Mean = Total Quantity/Total Items ​

9. Cheapest Exam Trick 

Assume total mixture = LCM of ratios

Ex: 3:2 → Assume 5 or 10 or 100.

Avoid fractions.

10. Percentage Conversion Trick

Convert ratio to % instantly:

Ratio	Percentage
1:1	50%
1:2	33.33%
2:3	40%
3:2	60%

Huge time saver.

11. If Ratio Becomes Smaller

Water increased OR milk removed.

12. If Ratio Becomes Larger

Milk increased OR water removed.

(Quick logical check!)

13. Successive Replacement Shortcut

If half is replaced twice:

Remaining = (1/2)² = ¼

No long steps needed.

14. Use Assumption Method

If percentage looks ugly (like 37%), assume total = 100 liters.

Makes math mental.

15. Difference Trick

If strength changes from 40% → 25%

Decrease = 15%

Means water added equals 15% of total.

16. Cross Multiplication Trick

For ratio change: Old Milk / Old Total = New Milk / New Total

Solve in ONE step.

17. Exam Favorite Pattern

Remove x liters, add water → find purity.

Immediately use:

Pure left = Original(1- x / Total)

18. Extreme Shortcut (No Formula)

Just track the pure quantity.

Examiners hide this — but it never changes unless removed.

19. LCM Mega Trick

When ratios like 7:13 appear → assume total = 20 or 200

Avoid decimals completely.

20. Golden Rule of Mixture Problems

Never track both liquids. Track ONLY the unchanged one.