Amal buys 110 kg of syrup and 120 kg of juice, syrup being 20% less costly than juice, per kg. He sells 10 kg of syrup at 10% profit and 20 kg of juice at 20% profit. Mixing the remaining juice and syrup, Amal sells the mixture at ₹308.32 per kg and makes an overall profit of 64%. Then, Amal's cost price for syrup, in rupees per kg, is
Question:
Amal buys 110 kg of syrup and 120 kg of juice, syrup being 20% less costly than juice, per kg. He sells 10 kg of syrup at 10% profit and 20 kg of juice at 20% profit. Mixing the remaining juice and syrup, Amal sells the mixture at ₹308.32 per kg and makes an overall profit of 64%. Then, Amal's cost price for syrup, in rupees per kg, is
Amal buys 110 kg of syrup and 120 kg of juice, syrup being 20% less costly than juice, per kg. He sells 10 kg of syrup at 10% profit and 20 kg of juice at 20% profit. Mixing the remaining juice and syrup, Amal sells the mixture at ₹308.32 per kg and makes an overall profit of 64%. Then, Amal's cost price for syrup, in rupees per kg, is
Options
Answer: 160
Explanation:
Let juice price = J (₹/kg), syrup price = S (₹/kg). S = 0.8J. Total cost = 110S + 120J = 110(0.8J) + 120J = 88J + 120J = 208J. Revenue: 10 kg syrup at 10% profit = 10 × 1.1S = 11S. 20 kg juice at 20% profit = 20 × 1.2J = 24J. Remaining 100 kg syrup + 100 kg juice = 200 kg mixture sold at 308.32/kg ⇒ 200 × 308.32 = 61664. Total revenue = 11S + 24J + 61664 = 11(0.8J) + 24J + 61664 = 8.8J + 24J + 61664 = 32.8J + 61664. Overall profit 64% ⇒ Revenue = 1.64 × Cost = 1.64 × 208J = 341.12J. So 32.8J + 61664 = 341.12J ⇒ 61664 = 308.32J ⇒ J = 61664 / 308.32 = 200. Therefore S = 0.8 × 200 = 160. Final Answer: 160
Explanation:
Let juice price = J (₹/kg), syrup price = S (₹/kg). S = 0.8J. Total cost = 110S + 120J = 110(0.8J) + 120J = 88J + 120J = 208J. Revenue: 10 kg syrup at 10% profit = 10 × 1.1S = 11S. 20 kg juice at 20% profit = 20 × 1.2J = 24J. Remaining 100 kg syrup + 100 kg juice = 200 kg mixture sold at 308.32/kg ⇒ 200 × 308.32 = 61664. Total revenue = 11S + 24J + 61664 = 11(0.8J) + 24J + 61664 = 8.8J + 24J + 61664 = 32.8J + 61664. Overall profit 64% ⇒ Revenue = 1.64 × Cost = 1.64 × 208J = 341.12J. So 32.8J + 61664 = 341.12J ⇒ 61664 = 308.32J ⇒ J = 61664 / 308.32 = 200. Therefore S = 0.8 × 200 = 160. Final Answer: 160
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