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

Step 1: Given Information

Amal purchases:

• 110 kg of syrup
• 120 kg of juice

The cost price of syrup is 20% less than that of juice.

 

Step 2: Assume Cost Prices

Let the cost price (CP) of 1 kg of juice be: \[ 10 \text{ CP} \] Since syrup is 20% less: \[ \text{CP of 1 kg syrup} = 10 - 20\% \text{ of } 10 = 8 \text{ CP} \]

Step 3: Selling Part of Syrup and Juice

Amal sells:

• 10 kg of syrup at 10% profit
• 20 kg of juice at 20% profit

Selling price of 10 kg syrup: \[ 10 \times 8 \times 1.1 = 88 \text{ CP} \] Selling price of 20 kg juice: \[ 20 \times 10 \times 1.2 = 240 \text{ CP} \]

 

Step 4: Selling the Remaining Mixture

Remaining quantity = \( (110 + 120) - (10 + 20) = 200 \text{ kg} \) Selling price per kg = ₹308.32 Total selling price of mixture: \[ 308.32 \times 200 = 61664 \text{ CP} \]

Step 5: Total Cost Price and Profit

Total cost price: \[ (110 \times 8) + (120 \times 10) = 880 + 1200 = 2080 \text{ CP} \] Given overall profit = 64% Total selling price: \[ 2080 \times \frac{164}{100} = 3411.20 \text{ CP} \] Already known: \[ \text{Selling price} = 88 + 240 + 61664 = 61992 \text{ CP} \] Therefore, solve for 1 CP: \[ 61992 = 2080 \times \frac{164}{100} \Rightarrow \text{CP unit} = ₹20 \]

Step 6: Find Cost Price of Syrup

Cost price of syrup per kg: \[ 8 \times 20 = \boxed{₹160} \]

Final Answer:

\[ \boxed{\text{Cost price of syrup = ₹160 per kg}} \]

Answer 2

Step 1: Given Purchase

Amal purchases:

• 110 kg of syrup
• 120 kg of juice

The cost price of syrup is 20% less than that of juice.

Step 2: Assume Cost Prices

Let the cost price (CP) of 1 kg of juice be: \[ 10 \text{ CP} \] Then, the cost price of 1 kg of syrup is: \[ 10 - 20\% \text{ of } 10 = 8 \text{ CP} \]

Step 3: Partial Sales with Profit

Amal sells:

• 10 kg of syrup at 10% profit:
• 20 kg of juice at 20% profit:

Step 4: Mixture Sale

Remaining quantity: \[ 110 - 10 = 100 \text{ kg syrup}, \quad 120 - 20 = 100 \text{ kg juice} \] Mixed quantity = 200 kg Selling price per kg = ₹308.32 Total SP for mixture: \[ 200 \times 308.32 = 61664 \]

Step 5: Total Cost & Profit

Total cost price: \[ 110 \times 8 + 120 \times 10 = 880 + 1200 = 2080 \text{ CP} \] Overall profit = 64% \[ \text{Total SP} = 2080 \times \frac{164}{100} = 3411.20 \] Known total SP = \[ 88 + 240 + 61664 = 61992 \] So CP unit: \[ \text{1 CP} = \frac{61992}{3411.2} = 20 \]

Step 6: Final Cost Price of Syrup

Cost price of 1 kg syrup: \[ 8 \times 20 = \boxed{₹160} \]

Final Answer:

\[ \boxed{\text{Cost price of syrup = ₹160 per kg}} \]