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

Let the cost price of juice per kg be 'J' rupees.

Since, syrup is 20% less costly than juice, the cost price of syrup per kg = 0.8J rupees.

Calculate the selling price:

⇒ Selling price of 10 kg syrup at 10% profit: 10 × 0.8J × 1.1 = 8.8J

⇒ Selling price of 20 kg juice at 20% profit: 20 × J × 1.2 = 24J

now, the Remaining quantities are syrup = 100 kg and juice = 100 kg

Total selling price of the remaining mixture:

⇒ Selling price per kg of the mixture: ₹308.32

⇒ Total selling price of the mixture: 200 × 308.32 = 61664 rupees

∴ Total selling price: 8.8J + 24J + 61664

Total cost price:

⇒ Cost price of syrup: 110 × 0.8J = 88J

⇒ Cost price of juice: 120J

⇒ Total cost price: 88J + 120J = 208J

∴ Overall profit:

⇒ Profit percentage: 64% (given)

⇒ Total profit: Total Selling Price - Total Cost Price

⇒ 1.64 × Total Cost Price = Total Selling Price

⇒ 1.64 × 208J = 8.8J + 24J + 61664

⇒ 341.12J = 32.8J + 61664

⇒ 308.32J = 61664

⇒ J = 61664 / 308.32

⇒ J = 200

Therefore, the cost price of syrup is = 0.8J = 160 rupees per kg