Mixture & Alligation (Arithmetic Mathematics)

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Q. In a 100-liter mixture, the ratio of milk to water is 3 : 2. How much more water must be added to make the ratio 1 : 2 ?

Options: (a) 120 L (b) 80 L (c) 60 L (d) 100 L

Ans: (d) 100 L

Solⁿ (Normal Method)

• Total mixture = 100 L


• Milk : Water = 3 : 2

Milk = $=60$ L
Water = $=40$ L

Now milk stays the same (60 L).
We need new ratio 1 : 2, meaning water must be double the milk.

Required water = $=120$ L

Already water = 40 L

Extra water needed = 120 − 40 = 80 L

Ans : (b) 80 L

Fast Trick (Exam Shortcut)

Trick Formula: When only water is added:

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

1st: Milk = 60
2nd: New ratio → Water = 2 × Milk = 120
3rd: Extra water = 120 − 40

Ans = 80 Liters

5-Second Ratio Trick (Best for Competitive Exams)

Convert old ratio to match milk:

Old → 3 : 2
New → 1 : 2

Make milk same:

Multiply new ratio by 60:

1 → 60
2 → 120

Water increases from 40 → 120

Increase = 80 L