In mixture A of 200 ml, there is 40% of milk and the rest is water while in mixture B of 300 ml, the ratio of milk and water is 3 : 7. When both the mixture is poured into another vessel C, then find the ratio of milk and water in vessel C.
- AOption (a)
20 : 27
- BOption (b)
17 : 29
- COption (c)
17 : 33
- DOption (d)
20 : 33
- EOption (e)
29 : 33
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Correct answer
17 : 33
Why this answer is correct
Shortcut Trick
Mixture A (200 ml): Milk = 40% of 200 = 80 ml, Water = 120 ml.
Mixture B (300 ml): Ratio 3 : 7 → Milk = (3/10) × 300 = 90 ml, Water = 210 ml.
Vessel C: Total Milk = 80 + 90 = 170 ml, Total Water = 120 + 210 = 330 ml.
Ratio in C = 170 : 330 = 17 : 33.
∴ The correct answer is 17 : 33.
Alternate Method
Given: Mixture A = 200 ml, Mixture B = 300 ml.
Step 1: Calculate components of Mixture A
⇒ Milk in A = 40% of 200 = (40/100) × 200 = 80 ml
⇒ Water in A = 200 − 80 = 120 ml
Step 2: Calculate components of Mixture B
⇒ Total Ratio = 3 + 7 = 10 units
⇒ 10 units = 300 ml ⇒ 1 unit = 30 ml
⇒ Milk in B = 3 × 30 = 90 ml
⇒ Water in B = 7 × 30 = 210 ml
Step 3: Combine in Vessel C
⇒ Total Milk = 80 + 90 = 170 ml
⇒ Total Water = 120 + 210 = 330 ml
⇒ Ratio M : W = 170 : 330 = 17 : 33
∴ The correct answer is 17 : 33.
Additional Information
Alligation Method
Used to find the ratio in which two mixtures of known concentrations should be mixed to get a final concentration, or vice versa.
Percentage to Ratio Conversion
A concentration of x% can be written as a ratio of x : (100 − x). For example, 40% milk means Milk : Water is 40 : 60 or 2 : 3.
Replacement Formula
Final Quantity = Initial Quantity × (1 − Removed/Total)n, where n is the number of operations.