Alliagations And Mixtures

Alliagations And Mixtures   

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Alligation - In this we find the proportion in which ingredients at given prices must be mixed to produce a mixture at a given price, this is termed as alligation. Alligation method can not be applied for absolute values, but it can be applied for Qestion related to Ratio, Rate, Percentage, Speed etc ( Means it can be applied for comparable values like per hour, per km , per kg etc. ) Rule of Alligation : If gradients are mixed in a ratio then we can write Ex. In what proportion must weat at Price 4.10 per kg must be mixed with weat at Price 4.60 per kg, so that the mixture be worth Rs 4.30 a Kg ? Solution : Here, CP of unit quantity of Dearer = 460 per kg , CP of unit quantity of Cheaper = 410 per kg So we can use above formuls : So, the required ratio be 3 : 2 Ex. How many kg of rice at Rs. 60 per kg, must be be mixed with 30 kg of rice at Rs 25 per kg, so that he may on selling the mixture at Rs 50 per kg gain 25 % on the outlay ? Solution : First we have to find cost price of mixture, as seller is gaining 25 % profit on mixture so its cost price will be Now use the formula of alligation to find to find out quantity of dearer rice, (Note : Here mean price will be CP of mixture, do not get confused by Selling price Rs 50 per kg ) Ex. A mixture of certain quantity of milk with 20 liters of water of worth Rs 10 per liter. If pure milk is of worth Rs 15 per liter, how much milk is there in the mixture ? Solution : By rule of alligation So, Quantity of milk will be 40 liters Ex. In what proportion must water be mixed with milk to gain 20 % by selling it at cost price ? Solution : Let cost price of milk be Rs 1 per liter, then S.P of mixture is also Rs 1 per liter Now CP of mixture be = 1 - ( 20 % of Rs 1 ) = 1 - ( 20 * 1 / 100 ) = 80 / 100 = Rs 4 / 5 Required ratio = 1 : 4 Question based on Mixture from two vessels ( Note : Frequently asked in MBA entrance exams ) Ex. Milk and water are mixed in a vessel A in the ratio 5 : 3 and in vessel B in ratio 9 : 7 . In what ratio should quantities be taken from the two vessels so as to form a mixture in which milk and water will be in the proportion of 7 : 5 ? Solution : In vessel A, milk = 5 / 5 + 3 = 5 / 8 of the weight of mixture In vessel B milk = 9 / 9 + 7 = 9 / 16 of the weight of mixture Now, we have to form a mixture in which milk be 7 / 12 of the weight of the mixture Now according to rule of alligation :           Ex. A goldsmith has two qualities of gold, one of 10 carats and another of 15 carates purity. In what proportion should he mix both to make an ornament of 12 carats purity ? Solution : By applying rule of alligations So both qualities of gold should be mixed in the ratio of 3 : 2 Ex. 400 gm spirit solution has 40 % spirit in it , How may grams of spirit should be added to make it 60 % in the solution ? Solution : By applying rule of alligations and mixtures So, the two mixtures should be added in ratio 2 : 1