Alligations and Mixtures Questions for CAT

A mixture of alcohol and water has a ratio of 4:5. If 18 litres of the solution is removed and replaced with alcohol, causing the ratio to reverse, what is the total volume of the initial mixture?

A vessel V1 contains a mixture of milk and water in a ratio of 7 : 3. If 20 liters of this mixture is taken out and poured into vessel V2 that already contains milk and water in the ratio 4 : 1, then the difference between total quantity of milk and water in V2 becomes 50 liters. Find the total quantity (in liters) of initial mixture in vessel V2.

A box contains 600 balls, each either red or blue. The number of metallic red balls equals the number of metallic blue balls. If 30% of the red balls and 45% of the blue balls are metallic, how many non-metallic balls are in the box?

Two types of rice are mixed in the ratio 2:3. The cheaper rice costs ₹24/kg and the costlier ₹36/kg. Find the average price per kg of the mixture.

A mixture of 40 litres has milk and water in ratio 3:1. Find the quantity of milk.

A grocer mixes two varieties of sugar costing ₹30/kg and ₹50/kg. If he wants to make a profit of 20% by selling the mixture at ₹48/kg, in what ratio should the two varieties be mixed?

A new coffee shop aims for 48% of customers by attracting them from BrewCafe (42%) and CoffeeHub (55%). Determine the ratio in which it should attract customers from BrewCafe and CoffeeHub.

Praveen combines three types of rice (Basmati=3x, Arborio=2x, Glutinous=x). Mixture B has a ratio of 6:3:1 and is priced at Rs.30/kg with a 20% profit. What is the cost price per kg of Mixture B?

Three solutions with acid percentages of 40%, 60%, and 80% are mixed in quantities of a, (a+1), and (a+2) liters, resulting in a final acid concentration of 64.444%. What is the value of a?

Two 900 cc bottles are filled with dye solutions of strengths 40% and 25%, respectively. A portion of the solution from the first bottle is discarded and replaced by an equal volume from the second bottle. If the strength of the dye solution in the first bottle becomes 34% after this operation, what is the volume, in cc, of the solution left in the second bottle?

One alloy has 84% copper and 16% zinc, while another has 88% copper, 8% zinc, and 4% aluminium. If these are combined to create an alloy with 13% zinc, what is the percentage of copper in the new alloy?

In a beaker, acid and water are mixed in a 2:5 ratio. How much acid should be added to this 210-liter solution to achieve a 40% acid concentration in the new solution?

Two varieties of rice are mixed in the ratio 4:3. The cheaper costs ₹28/kg and the dearer ₹35/kg. Find the average price per kg of the mixture.

Two containers contain mixtures of alcohol and water in ratios 5:3 and 7:5. If equal volumes are mixed, what is the final ratio of alcohol to water?

A 25% ethanol solution is mixed with another ethanol solution, U, of unknown concentration in the ratio 2:1 by volume. The resulting mixture is then combined with an equal volume of a 35% ethanol solution. If the final mixture is 40% ethanol, what is the concentration of solution U?

In March 2011, EF Public Library purchased a total of 15 new books published in 2010 with a total expenditure of Rs. 4500. Of these books, 13 books were purchased from MN Distributors, while the remaining two were purchased from UV Publishers. It is observed that one-sixth of the average price of all the 15 books purchased is equal to one-fifth of the average price of the 13 books obtained from MN Distributors. Of the two books obtained from UV Publishers, if one-third of the price of one volume is equal to one-half of the price of the other, then the price of the two books are:

An alloy of gold and copper of unknown weight is mixed with 1.5 kg of pure gold to form a new alloy that is 90% gold by weight. If the same weight of the initial alloy is instead mixed with 2 kg of another alloy that is 81% gold, the resulting alloy is 84% gold. What is the weight (in kg) of the initial alloy?

A vessel contains only milk. Nine litres of the liquid are removed and replaced with water, and the same operation is repeated once. If the final ratio of milk to water becomes 4:5, then the capacity of the vessel, in litres, is

A 20% ethanol solution is mixed with another ethanol solution of unknown strength $S\%$ in the ratio $2:3$ by volume to form mixture $M$. An equal volume of a 35% ethanol solution is then added to $M$. If the final mixture is $41\%$ ethanol, what is the value of $S$?

An alloy weighing 65 kg consists of two metals, iron and silver, in a certain ratio. The price per kg of iron and silver is in the ratio 2:5. If the weight ratio is interchanged (keeping the total weight same), the total price increases by (\tfrac{15}{38})th of the previous amount. Find the weight of silver in the original alloy (in kg).