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

Two identical jars are filled with alcohol solutions. The ratio of the volume of alcohol to the volume of water is $p : 1$ in one jar and $q : 1$ in the other jar. If the entire contents of the two jars are mixed/ together, then what is the ratio of the volume of alcohol to the volume of water in the mixture?
  1. $\displaystyle\frac{p+q+2pq}{p+q+2}$
  2. $\displaystyle\frac{p+q}{p+q+2}$
  3. $\displaystyle\frac{p+q+1}{p+q+2}$

  4. None of these
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Jar 1: Alcohol = p/(p+1), Water = 1/(p+1). Jar 2: Alcohol = q/(q+1), Water = 1/(q+1). Total Alcohol = p/(p+1) + q/(q+1) = (pq+p+pq+q)/((p+1)(q+1)). Total Water = 1/(p+1) + 1/(q+1) = (q+1+p+1)/((p+1)(q+1)). Ratio = (2pq+p+q)/(p+q+2).

Multiple choice

From a container of milk, $5$ litres of milk is replaced with $5$ litres of water. This process is repeated again. Thus in two attempts the ratio of milk and water became $81:19.$ The initial amount of milk in the container was
  1. $50$ litres
  2. $45$ litres
  3. $40$ litres
  4. $25$ litres
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Let initial milk be x. After two replacements of 5L, final milk = x(1 - 5/x)^2. Ratio of milk to total is 81/100. So, (1 - 5/x)^2 = 81/100. Taking square root, 1 - 5/x = 9/10. 5/x = 1/10, so x = 50.

Multiple choice

The proportion of milk and water in $3$ samples is $2:1,\,3:2$ and $5:3$. A mixture comprising of equal quantities of all $3$ samples is made. The proportion of milk and water in the mixture is
  1. $227:133$
  2. $133:227$
  3. $99:61$
  4. $61:99$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Samples have milk/water ratios 2:1, 3:2, 5:3. Fractions of milk are 2/3, 3/5, 5/8. Average milk = (2/3 + 3/5 + 5/8) / 3 = (80 + 72 + 75) / 120 / 3 = 227 / 360. Milk = 227, Water = 360 - 227 = 133. Ratio = 227:133.

Multiple choice

Flour, water, and salt are mixed by weight in the ratio of $5:4:1$, respectively, to produce a certain type of dough. In order to make $5$ pounds of this dough, what weight of salt, in pounds, is required?
  1. $\displaystyle\frac{1}{4}$
  2. $\displaystyle\frac{1}{2}$
  3. $\displaystyle\frac{3}{4}$
  4. $1$
  5. $2$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

The ratio is 5:4:1, total parts = 10. Salt is 1/10 of the total weight. For 5 pounds of dough, salt = 5 * (1/10) = 0.5 pounds.

Multiple choice

The total weight of a gas mixture which contains $11.2$ litres of $CO_{2}$, $5.6$ litres of $O_{2}$, $22.4$ litres of $N_{2}$, $44.8$ litres of $He$ at $0^{o}C$ and $760$ $mm$ of $Hg$ pressure is:
  1. $44$ $g$
  2. $22$ $g$
  3. $33$ $g$
  4. $66$ $g$
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

At STP, 22.4 L = 1 mole. Moles: CO2 = 0.5, O2 = 0.25, N2 = 1, He = 2. Masses: CO2 = 0.5 * 44 = 22g, O2 = 0.25 * 32 = 8g, N2 = 1 * 28 = 28g, He = 2 * 4 = 8g. Total mass = 22 + 8 + 28 + 8 = 66g.