Mixture & Alligation (Arithmetic Mathematics) : āĻŽāĻŋāĻļā§ā§°āĻŖ āĻā§°ā§ āĻāĻ˛āĻŋāĻā§āĻāĻ¨ (āĻĒāĻžāĻā§āĻāĻŖāĻŋāĻ¤)
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 ? āĻĒā§ā§°āĻļā§āĻ¨: 100 āĻ˛āĻŋāĻāĻžā§° āĻŽāĻŋāĻļā§ā§°āĻŖāĻ¤ āĻāĻžāĻā§ā§° : āĻĒāĻžāĻ¨ā§ = 3 : 2āĨ¤ āĻ āĻ¨ā§āĻĒāĻžāĻ¤ 1 : 2 āĻā§°āĻŋāĻŦāĻ˛ā§ āĻā§°ā§ āĻāĻŋāĻŽāĻžāĻ¨ āĻ˛āĻŋāĻāĻžā§° āĻĒāĻžāĻ¨ā§ āĻ¯ā§āĻ āĻā§°āĻŋāĻŦ āĻ˛āĻžāĻāĻŋāĻŦ ?
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 = 3/5×100 L
Water = 2/5 × 100 L
Now milk stays the same (60 L).
We need new ratio 1 : 2, meaning water must be double the milk.
Required water = 2 × 60 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: āĻ¸āĻšāĻ āĻ¸ā§āĻ¤ā§ā§°: āĻā§ā§ąāĻ˛ āĻĒāĻžāĻ¨ā§ āĻ¯ā§āĻ āĻā§°āĻŋāĻ˛ā§
Extra Water = (Milk × New Water Ratio / New Milk Ratio) − Old Water
āĻ āĻ¤āĻŋā§°āĻŋāĻā§āĻ¤ āĻĒāĻžāĻ¨ā§ = (āĻāĻžāĻā§ā§° × āĻ¨āĻ¤ā§āĻ¨ āĻĒāĻžāĻ¨ā§ā§° āĻ āĻāĻļ / āĻ¨āĻ¤ā§āĻ¨ āĻāĻžāĻā§ā§°ā§° āĻ āĻāĻļ) − āĻĒā§ā§°āĻŖāĻŋ āĻĒāĻžāĻ¨ā§
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) : ā§Ģ āĻā§āĻā§āĻŖā§āĻĄā§° Ratio Trick (āĻĒā§ā§°āĻ¤āĻŋāĻ¯ā§āĻāĻŋāĻ¤āĻžāĻŽā§āĻ˛āĻ āĻĒā§°ā§āĻā§āĻˇāĻžā§° āĻŦāĻžāĻŦā§ āĻ¸ā§°ā§āĻŦā§āĻ¤ā§āĻ¤āĻŽ āĻā§āĻļāĻ˛)
Convert old ratio to match milk : āĻāĻžāĻā§ā§° āĻāĻā§ ā§°āĻžāĻāĻŋ āĻĒā§ā§°āĻŖāĻŋ āĻ āĻ¨ā§āĻĒāĻžāĻ¤ ā§°ā§āĻĒāĻžāĻ¨ā§āĻ¤ā§° āĻā§°āĻ
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