  Question

Coffee costing $$Rs. 250$$ per $$kg$$ was mixed with chicory costing $$Rs. 75$$ per $$kg$$ in the ratio $$5:2$$ for a certain blend. If the mixture was sold at $$Rs. 230$$ per $$kg$$ , find the gain or loss per cent.

Solution

cost of coffee$$= 250\ per\ kg$$.cost of chicory $$= 75\ per\ kg$$coffee: chicory $$5:2$$if the weight of mixture is $$1\ kg.$$$$\dfrac{5x+2x}{7}=1$$$$\Rightarrow 7x=7$$$$\Rightarrow x=1$$$$\therefore$$ weight of coffee = $$\dfrac{5x}{7}=\dfrac{5}{7}\ kg$$weight of chicory = $$\dfrac{2x}{7}=\dfrac{2}{7}\ kg$$cost of $$\dfrac{5}{7}$$ kg coffee = $$\dfrac{5}{7}\times 250=\dfrac{1250}{7}$$cost of $$\dfrac{2}{7}$$ kg chicory = $$\dfrac{2}{7}\times 75=\dfrac{150}{7}$$total cost of $$1\ kg$$ mixture = $$\dfrac{1250}{7}+\dfrac{150}{7}$$cost price of $$1\ kg$$ mixture = $$\dfrac{1400}{7}=200\ Rs$$selling of $$1$$ kg minute = $$230\ Rs$$gain or loss = $$\dfrac{SP-CP}{CP}\times 100=\dfrac{230-200}{200}\times 100$$= $$\dfrac{30}{2}= 15$$%since its positive, the mixture was sold at a gain of $$15\%$$.Mathematics

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