CAT 2022 Slot 1 Paper

Total syrup - $110\,\text{kg}$ Total juice $-120\,\text{kg}$ It is given, cost price of syrup is $20\%$ less than the cost price of juice. Let the cost price of juice per $\text{kg}$ be $10\,\text{CP}$ Cost price of syrup per $\text{kg}$ is $8\,\text{CP}$ $10\,\text{kg}$ syrup → cost price $=80\,\text{CP}$ It is given, $10\,\text{kg}$ syrup is sold at $10\%$ profit. This implies selling price $=1.1\times 80\,\text{CP}=88\,\text{CP}$ $20\,\text{kg}$ juice → cost price $=200\,\text{CP}$ It is given, $20\,\text{kg}$ juice is sold at $20\%$ profit. This implies selling price $=1.2 \times 200\,\text{CP}=$ $240\,\text{CP}$ It is given, Mixing the remaining juice and syrup, Amal sells the mixture at $\text{Rs.}\,308.32$ per $\text{kg}$ Selling price of the remaining mixture $=308.32 \times 200 = \text{Rs}\,61664$ Total $\text{S.P.}$ $=61664+328\,\text{CP}$ Total $\text{C.P.}$ $=880\,\text{CP}+1200\,\text{CP}=2080\,\text{CP}$ Overall profit $=64\%$ $61664+328\,\text{CP}=\;\frac{164}{100}(2080\,\text{CP})$ Solving, we get $\text{CP}=20$ Cost price for syrup per $\text{kg}=8\,\text{CP}=8 \times 20=$ Rs 160