Application of Alligation in Mixtures Solutions and Concept of Replacement

In this I have applied the concepts that I have explained in my previous video to solve the questions of Mixtures and Solutions. I have told how the percentage equivalent and its fractions equivalent should be used while solving questions of Mixtures and Solutions. After that I have told the concept of replacement in which I have dealt with those type of questions in which a liquid is replaced by another liquid again and again and we have to finally find out how much liquid is left at the end in terms of exact quantity or in terms of percentage or in terms of fraction, depends what the questions is asking and what information is given. Your comments and suggestions are most welcome. The questions discussed are listed below.

Question 1. Two vessels contain spirit and water mixed respectively in the ratio 1:3 and 3:5 . Find the ratio in which these are to be mixed to get a new mixture in which the ratio of spirit to water is 1:2 ?

Question 2. These are two kinds of alloys of Iron and Lead. The first alloy contains 93.33 % iron and the remaining is lead whereas second alloy contains 86.66 % iron and rest is lead. What weight of the first alloy should be mixed with some weight of the second alloy so as to make a 50 kg mass containing 90 % iron ?

Question 3. Two containers of equal capacity are full of a mixture of oil and water. In the first, the ratio of oil to water is 4:7 and in the second, the ratio is 7:11 . Now both the mixtures are mixed in a bigger container. What is the resulting ratio of oil to water ?

Question 4. A man buys milk at Rs. 8.5 per litre and dilutes it with water. He sells the mixture at the same rate and thus gains 11.11 % . Find the quantity of water mixed by him in every litre of milk ?

Question 5. In what ratio should water be mixed with soda costing Rs. 12 per litre so as to make a profit of 25 % by selling the dilated liquid at Rs. 13.75 per litre ?

Question 6. What will be the ratio of milk and water in the final solution formed by mixing milk and water that are present in three vessels of equal capacities in the ratios 5:2, 4:1 and 6:1 respectively ?

Question 7. In what proportion must water be mixed with milk so as to gain 20 % by selling the mixture at the cost price of the milk assuming water to be free ??

Question 8. A milkman cheated his customer by stealing milk from the bottle and replacing it with milk of 20 % concentration. The bottle at the end has the concentration of milk as 25 %. How much percent of the milk bottle had the milkman replaced given the original concentration of the milk in the bottle to be 50 % ?

Question 9. Two containers contain a mixture of wine and water. In the first container the ratio of wine is to water is 8:3 and in the second container the ratio is 5:1 . A 35 litre cask is filled from these containers so as to contain a mixture of wine and water in the ratio 4:1. How many litres are taken from the first container to fill these 35 litres ?

Question 10. Each of two vessels V1 and V2 has 20 litres of a solution of milk and water. V1 has 10 % water and certain quantity of water is added to it so as to raise the %age of water to 25 %. V2 has milk and water in the ratio 3:2 and certain quantity of water is added to it so as to reverse this ratio. What is the difference between the quantity of water added to V1 and that added to V2 ?

Questions based on the Concept of Replacement -

Question 11. A tank contains 50 litres of water. 5 litre of water is taken out of it and replaced by milk. The process is repeated again. Find the proportion of milk and water in the resulting mixture ?

Question 12. Ten litres are drawn from a container full of water and replaced by pure milk. Again 10 litres of solution is drawn off and substituted by pure milk. The container now contains milk and water in the ratio 9:16 . What is the capacity of the container ?

Question 13. 60 litres of spirit is drawn from 600 litres of spirit and replaced with water. Sixty litres of the mixture is then drawn and replaced with water and this procedure is repeated once more. Find the present quantity of spirit in the mixture ?

Your comments and suggestions are most welcome. You can also ask your doubts in the comment section below.