Question:medium

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

Updated On: Jan 15, 2026
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Correct Answer: 160

Solution and Explanation

Step 1: Given Information

Amal's purchases:

  • 110 kg of syrup
  • 120 kg of juice

The cost price of syrup is 20% less than the cost price 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 expensive:

Cost price of 1 kg syrup = \( 10 - 0.20 \times 10 = 8 \text{ CP} \)

Step 3: Selling Part of Syrup and Juice

Amal sells:

  • 10 kg of syrup at a 10% profit
  • 20 kg of juice at a 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 = \( 2080 \times \frac{100 + 64}{100} = 2080 \times 1.64 = 3411.20 \text{ CP} \)

Calculated selling price = \( 88 + 240 + 61664 = 61992 \text{ CP} \)

Equating the total selling price to find the value of 1 CP unit:

\( 61992 \text{ CP} = 2080 \times 1.64 \text{ CP} \implies \text{CP unit} = ₹20 \)

Step 6: Find Cost Price of Syrup

Cost price of syrup per kg: \( 8 \times \text{CP unit} = 8 \times 20 = \boxed{₹160} \)

Final Answer:

Cost price of syrup = ₹160 per kg

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In the dynamic realm of creativity, artists often find themselves at the crossroads between drawing inspiration from diverse cultures and inadvertently crossing into the territory of cultural appropriation. Inspiration is the lifeblood of creativity, driving artists to create works that resonate across borders. In a globalized era of the modern world, artists draw from a vast array of cultural influences. When approached respectfully, inspiration becomes a bridge, fostering understanding and appreciation of cultural diversity. However, the line between inspiration and cultural appropriation can be thin and easily blurred.
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