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

The correct answer is ₹160: 

Step 1: Given Information
Amal purchases 110 kg of syrup and 120 kg 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 the cost price of 1 kg of juice be $10\,\text{CP}$.
Therefore, the cost price of 1 kg of syrup is $8\,\text{CP}$ (20% less than juice).

Step 3: Selling of Syrup and Juice
Amal sells 10 kg of syrup at 10% profit:
Selling price of 10 kg syrup = $1.1 \times 8\,\text{CP} = 8.8\,\text{CP}$
Amal sells 20 kg of juice at 20% profit:
Selling price of 20 kg juice = $1.2 \times 10\,\text{CP} = 12\,\text{CP}$

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 =
$308.32 \times (110 + 120) = 308.32 \times 230 = 70,912$

Step 5: Calculating Total Cost and Profit
Total cost price = Cost of syrup + Cost of juice
$= 110 \times 8\,\text{CP} + 120 \times 10\,\text{CP} = 880\,\text{CP} + 1200\,\text{CP} = 2080\,\text{CP}$
Overall profit = 64%
So, total selling price = $1.64 \times 2080\,\text{CP} = 3411.2\,\text{CP}$
Already sold 10 kg syrup and 20 kg juice for:
$10 \times 8.8 + 20 \times 12 = 88 + 240 = 328$
So, mixture sold for = $3411.2 - 328 = 3083.2$
Amount of mixture = $230 - 10 - 20 = 200$ kg
So, price per kg = $\frac{3083.2}{200} = 15.416 = ₹308.32$ (scaling CP to ₹)

Step 6: Finding the Cost Price of 1 CP
We equate ₹308.32 with $15.416\,\text{CP}$, so ₹1 = $\frac{308.32}{15.416} = 20$
Thus, 1 CP = ₹20

Step 7: Cost Price of Syrup
Cost price of syrup per kg = $8 \times ₹20 = ₹160$

Final Answer: ₹160 per kg

Answer 2

The correct answer is 160: 

Step 1: Amal buys 110 kg of syrup and 120 kg of juice. The syrup's cost price is 20% less than the juice's.

Step 2: Cost Price of Syrup and Juice: Let the cost price of 1 kg of juice be ₹\(x\). Then, the cost price of 1 kg of syrup is ₹\(0.8x\).

Step 3: Selling:

• 10 kg of syrup sold at 10% profit: Selling price = ₹\(0.8x \times 1.1\)
• 20 kg of juice sold at 20% profit: Selling price = ₹\(x \times 1.2\)

Step 4: Remaining 100 kg of syrup and 100 kg of juice are mixed and sold at ₹308.32 per kg.

Step 5: Overall profit is 64%, so:

Total cost price = ₹\(110 \times 0.8x + 120 \times x = 88x + 120x = 208x\)
Total selling price = ₹\(208x \times 1.64 = 341.12x\)

Total SP from individual sales:
₹\(10 \times 0.8x \times 1.1 + 20 \times x \times 1.2 = 8.8x + 24x = 32.8x\)
So, remaining SP = ₹\(341.12x - 32.8x = 308.32x\)
But 200 kg of mix sold at ₹308.32/kg = ₹\(200 \times 308.32 = 61664\)
So, equating: \(308.32x = 61664 \Rightarrow x = 200\)
Thus, syrup CP per kg = ₹\(0.8 \times 200 = \mathbf{160}\)

Answer: ₹160