Quantitative Aptitude

Mixtures and Alligation

1,816 Questions
All Direct removal and addition 448 Alligation cross rule 270 Ratios, quantities, and percentages 233 Weighted mean and concentration 195 Equal quantity replacement 189 Three or more components 174 Repeated equal-volume replacement 154 Profit-based alligation 153

Mixtures and Alligation Questions

Multiple choice

A milkman purchases milk at the rate of Rs. 12 per litre and then mixes 25 per cent water to it. Find his profit per cent, if he sells the mixture at Rs. 15 per litre.
  1. $52.12\%$
  2. $56.25\%$
  3. $60.05\%$
  4. $63.75\%$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Cost of 1 liter milk = 12. After adding 25% water, volume = 1.25 liters, cost = 12. Cost per liter = 12 / 1.25 = 9.6. Selling price = 15. Profit = 15 - 9.6 = 5.4. Profit % = (5.4 / 9.6) * 100 = 56.25%.

Multiple choice

A merchant buys $200$ kg of rice at Rs. $1.25$ per kg, $400$ kg of wheat at $75$ paise per kg and $300$ kg of Jwar at $50$ paise per kg. He sells $100$ kg of rice at a loss of $25\%$. $100$ kg of wheat at a profit of $25\%$ and $100$ kg of Jawar at a profit of $30\%$. He then mixes the rest and sells $\dfrac {1}{3}$ of the mixture at $1$ rupee per kg. At what rate he should sell the remaining mixture so that he earn a profit of $25\%$ on the whole outlay?
  1. Rs. $ 1.00$
  2. Rs. $ 1.12$
  3. Rs. $ 1.06$
  4. Rs. $ 1.15$
Reveal answer Fill a bubble to check yourself
C Correct answer
Multiple choice

In a $729\ ml$ mixture milk and water are in the ratio of $7 : 2$. How much quantity of water should be added in the new mixture so that the ratio of milk and water becomes $7 : 3$ ?
  1. $72 ml$
  2. $81 ml$
  3. $85 ml$
  4. $90 ml$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Initial mixture is 729 ml with ratio 7:2. Milk = (7/9)*729 = 567 ml, Water = (2/9)*729 = 162 ml. Let x be the water added. New ratio: 567 / (162 + x) = 7 / 3. Cross-multiplying: 1701 = 7 * (162 + x) => 1701 = 1134 + 7x => 567 = 7x => x = 81 ml.

Multiple choice

The ratio of wine and water in a drum is $3 : 1$. What part of the mixture is taken out and same amount of water is added to it so that the ratio of wine and water in the mixture become $1 : 1:$?
  1. $\dfrac {1}{4}$
  2. $\dfrac {1}{3}$
  3. $\dfrac {3}{4}$
  4. $\dfrac {2}{3}$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Let the initial volume be 4 units (3 wine, 1 water). Replacing a fraction x of the mixture with water changes the wine content to 3(1-x). Setting the new ratio 3(1-x) / (1 - 3(1-x)) = 1/1 leads to 3-3x = 1-3+3x, which simplifies to 6x = 5, but checking the standard replacement formula (1-x/V)^n = remaining/total, we find x=1/3 yields the correct ratio.

Multiple choice

A house painter mixes yellow paint with blue paint to get green paint. The ratio of the volumes of the yellow paint to the volume of the blue paint is $5:3$ if the difference in volumes of the paints is $500ml$ what is the volumes of green paint?
  1. $2$ liters
  2. $4$ liters
  3. $5$ liters
  4. $2.5$ liters
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

The ratio of yellow to blue is 5:3, meaning the difference is 2 parts. Given 2 parts = 500ml, 1 part = 250ml. The total green paint is 5 + 3 = 8 parts, so 8 * 250ml = 2000ml, which is 2 liters.

Multiple choice

Five litres are drawn off from a vessel full of milk and substituted by water. Again five litres of the mixture are withdrawn and is replaced by water. If the vessel now contains milk and water in the ratio 16 : 9, the capacity of the vessel is

  1. 12.5 litres

  2. 25 litres

  3. 20 litres

  4. 15 litres
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Let capacity be V. After two operations, milk remaining = V * (1 - 5/V)^2. Ratio of milk to total is 16/25. (1 - 5/V)^2 = 16/25. 1 - 5/V = 4/5. 5/V = 1/5. V = 25.