CAPF AC 2021 Q97: General Mental Ability – Quantitative Aptitude
How much water is to be added to 75 ml of alcohol so that the mixture contains 25% of alcohol?
- (a) 100 ml
- (b) 225 ml
- (c) 250 ml
- (d) 125 ml
Answer: (b) 225 ml
Explanation
Diluting alcohol with water
Given: water is added to 75 ml of alcohol so that the mixture has 25% alcohol; find the water to be added.
How to think: the amount of alcohol does not change.
Only the total grows.
So 75 ml must become one-quarter of the new mixture.
| Step | Working |
|---|---|
| Alcohol | 75 ml, stays the same |
| Alcohol is 25% of the mixture | Mixture = 75 ÷ 0.25 = 300 ml |
| Water to add | 300 − 75 = 225 ml |
Check: 75 out of 300 is 25%.
Shortcut: 25% alcohol means alcohol : water = 1 : 3.
So water = 3 × 75 = 225 ml.
Answer: (b) 225 ml.
Why each option is right or wrong
- (a) Incorrect. 100 ml of water gives 75 out of 175, which is about 43% alcohol.
- (b) CORRECT. The mixture must be 300 ml, so 225 ml of water is added.
- (c) Incorrect. 250 ml of water gives 75 out of 325, which is about 23% alcohol.
- (d) Incorrect. 125 ml of water gives 75 out of 200, which is 37.5% alcohol.
Key point
When only water is added, the quantity of the pure substance is constant. New total = pure quantity ÷ required fraction. Water added = new total − old total.
Remember
25% alcohol = 1 part alcohol : 3 parts water.
Common mistakes
- Giving the total mixture (300 ml) instead of the water added.
- Taking 25% of 75 ml, as if the alcohol itself were being reduced.
- Reading 25% as the share of water instead of the share of alcohol.
Exam tip
Educated guess: 25% alcohol means three parts water for each part of alcohol. Three times 75 is 225.
Sources
- NCERT Class VII Mathematics — Comparing Quantities (percentage)
- R. S. Aggarwal, Quantitative Aptitude — Alligation or Mixture