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Similar triangles are confusing me, specially the naming part, for instance, if it is given, triangles ABC and DEF are similar. If angle C is equal to angle E, AB is 4.2, DE is 2.1, BC is 6.4 and DF is 2.8 then find EF and AC. In the solution they have written AB/DE=BC/EF=AC/DF. But if angle C is equal to angle E then wont it be AB/DF? Since we take corresponding sides to equal angles,

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A shopkeeper marks his good at 60% above the cost price. He allows a discount of 12 1/2%. Also he cheats 14 2/7% while purchasing and 20%at selling and gives one article free on purchase of 15 articles. Find the profit/loss in whole transaction.

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Fresh grapes have 75% water and the rest is pulp. During the process of drying, it was found that at a particular stage it contained 50% water by weight. What is the percentage reduction in the weight of the original quantity of fresh grapes?

How many terms are there in the expression (1 + x2 + x4)10 when it is expanded?

In how many ways can five integers be selected out of the first 30 natural numbers so that their product ends with five?

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How do i solve inequalities and coded inequalities?