Question

Amal buys 110kg of syrup and 120kg of juice, syrup being 20% less costly than juice, per kg. He sells 10kg of syrup at 10% profit and 20kg 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

Answer 1

Correct Answer: 160

The correct answer is 160:
Step 1: Given Information
Amal purchases 110kg of syrup and 120kg of juice.
The cost price of syrup is 20% less than the cost price of juice.
Step 2: Cost Price of Syrup and Juice
Let's denote the cost price of 1 kg of juice as 10CP.
Therefore, the cost price of 1 kg of syrup is 8CP, as it is 20% less than the juice.
Step 3: Selling of Syrup and Juice
Amal sells 10kg of syrup at a 10% profit:
Selling price of 10kg syrup = \(1.1\times8CP=8.8CP\)
Amal sells 20kg of juice at a 20% profit:
Selling price of 20kg juice=\(1.2\times10CP=12CP\)
Step 4: Selling the Mixture
Amal combines the remaining syrup and juice and sells the mixture at ₹308.32 per kg.
Total selling price of the mixture = \(308.32\times(110 + 120) = 61664CP\)
Step 5: Calculating Total Cost and Profit
Total cost price=Cost price of syrup+Cost price of juice
Total cost price=\(110\times8CP+120\times10CP=2080CP\)
Overall profit = 64%
\(61664CP+328CP=164/100\times2080CP\)
Solving for CP, we find CP = 20.
Step 6: Cost Price of Syrup
Cost price for syrup per kg = \(8CP = 8\times20 = ₹160\).
Hence, the cost price for syrup is ₹160 per kg.

Answer 2

The correct answer is 160:
Step 1: Amal buys 110kg of syrup and 120kg of juice. The syrup's cost price is 20% less than the juice's.
Step 2: Cost Price of Syrup and Juice: Let's call the cost price of 1 kg of juice 10CP. So, syrup's cost price per kg is 8CP, being 20% less.
Step 3: Selling of Syrup and Juice: Amal sells 10kg of syrup at a 10% profit and 20kg of juice at a 20% profit.
Step 4: Selling the Mixture: The remaining syrup and juice are mixed and sold at ₹308.32 per kg.
Step 5: Calculating Total Cost and Profit: Total cost price is the sum of syrup and juice cost prices. The overall profit is 64%.
Step 6: Cost Price of Syrup: The cost price of syrup per kg is ₹160.
So, the cost price for syrup is ₹160 per kg.