Mixture and Alligation Exercise 1

Gold is 19 times as heavy as water and copper is 9 times heavy. In what ratio must these metals be mixed so that the mixture may be 15 times as heavy as water?

In a mixture of 45 litres, the ratio of milk and water is 3 : 2. How much water must be added to make the ratio 9 : 11?

In a mixture of 45 litres, the ratio of milk and water is 4 : 1. How much water must be added to make the mixture ratio 3 : 2?

A mixture (40 litres) contains tonic and water in the ratio 3 : 1. To make the ratio 7 : 2, how much additional amount of water is required?

An alloy contains copper and zinc in the ratio 5 : 3 and another alloy contains copper and tin in the ratio 8 : 5. If equal weights of both the alloys are melted together, then the weight of tin in the resulting alloy per unit will be:

In three vessels, the ratio of water and milk is 6 : 7, 5 : 9 and 8 : 7, respectively. If the mixtures of the three vessels are mixed together, then what will be the ratio of water and milk?

A jar of oil was four fifths full. When six bottles of oil were taken out and four bottles of oil were poured into, it was three fourths full. How many bottles of oil were contained by the jar?

A cane contains a mixture of two liquids A and B in the ratio 7 : 5. When 9 litres of mixture are drawn off and the cane is filled with B, the ratio of A and B becomes 7 : 9. How many litres of liquid A was contained by the cane initially?

A vessel is fully filled with a special liquid. Four litres of liquid is drawn out of this vessel and is replaced with water. If the ratio of the special liquid to the water becomes 1: 2, then what is the capacity the vessel?

Two equal glasses filled with mixtures of alcohol and water in the proportions of 2 : 1 and 1 : 1 respectively were emptied into third glass. What is the proportion of alcohol and water in the third glass?

A mixture of Nitric acid and Sulfuric acid is taken in the ratio of 1 : 2 and another mixture of the same is taken in the ratio 2 : 3. How many parts of the two mixtures must be taken to attain a new mixture consisting of Nitric acid and Sulfuric acid in the ratio of 3 : 5?

Several litres of acid were drawn off from a 54 litre vessel, full of acid and equal amount of water was added. Again the same volume of the mixture was drawn off and replaced by water. As a result now, the vessel contained 24 litres of pure acid. How much of the acid was drawn off initially?

Two vessels contain mixtures of milk and water in the ratio of 8 : 1 and 1 : 5 respectively. The contents of both of these are mixed in a specific ratio into a third vessel. How much mixture must be drawn from the second vessel to fill the third vessel (capacity 26 gallons) completely in order that the resulting mixture may be half milk and half water?

A container contains 40 litres of milk. From this container, 4 litres of milk was taken out and replaced by water. This process was repeated further two times. How much milk is now contained by the container?

Three containers A, B and C are having mixtures of milk and water in the ratio 1 : 5, 3 : 5 and 5 : 7, respectively. If the capacities of the containers are in the ratio 5 : 4 : 5, then find the ratio of the milk to the water if the mixtures of all the three containers are mixed together.

Tea worth ₹126 per kg and ₹135 per kg are mixed with a third variety in the ratio 1 : 1 : 2. If the mixture is worth ₹153 per kg, then the price of the third variety per kg is:

How much water must be added to 60 litres of milk at 1½ litres for ₹20 so as to have a mixture worth ₹10⅔ a litre?

Pure milk costs ₹3.60 per litre. A milkman adds water to 25 litres of pure milk and sells the mixture at ₹3 per litre. How many litres of water does he add?

Sameer bought 10 kg of tea at ₹45 per kg and 8 kg at ₹50 per kg. He mixed both the brands and sold it at a total profit of ₹32. What was the selling price per kg of the mixture?

A mixture consists of 15 parts of coffee, purchased at ₹2.10 per kg and 1 part of chicory, purchased at 98 paise per kg. If it is sold at ₹2.25 per kg, what profit would be made on the sale of 5 quintals?