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Allegations and Mixtures

Concepts Examples How To Solve Allegations Suppose the average weight of a group of objects O 1 is A 1 and average weight of group of objects O 2 is A 2 and A 1 2 , then we can write the data in the manner as shown in the figure. (A w −A 2 ) : (A w −A 1 ) gives the ratio of O 1 : O 2 . Allegations does not give the actual volume to be mixed but only the ratio in which volumes are to be mixed. Question 1 A shopkeeper sells two types of rice A and B. If he sold 30% of type A rice at a profit of 50% and sold 90% of the rice of type B at a profit of 10%. What is the averge profit percent of the shopkeeper, if he sells only these two types of rice. 35% ...

Weighted Averages

Concepts Examples When we have to calculate the average of some groups of different things, having different number of elements is being calculated, then it is called the weighted average. If the number of elements in n different groups be N 1 ,N 2 ,N 3 .. N n and their respective averages be A 1 ,A 2 ,A 3 ...A n , then Weighted average = $\frac{\mathbb{N}_1\cdot A_1+\mathbb{N}_2\cdot A_2+\mathbb{N}_3\cdot A_3...\mathbb{N}_n\cdot A_n}{\mathbb{N}_1+\mathbb{N}_2+\mathbb{N}_3...\mathbb{N}_n}$ N 1 · A 1 + N 2 · A 2 + N 3 · A 3 . . . N n · A n N 1 + N 2 + N 3 . . . N n   Question 1 Average cost of buying 5 quality A crackers is 60 and cost of buying 10 quality B crackers is 80. WHhat will be average cost of buying all the crackers. 71.33 ...