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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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