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
Explanation:
Let the cost price of juice be Rs. 10x/kg, hence cost price of syrup = 8x/kg
10 kg syrup is sold at 10% profit i.e., at 8.8x/kg. ∴ Total selling price = Rs. 88x
20 kg of juice is sold at 20% profit i.e., at 12x/kg ∴ Total selling price = Rs. 240x
Remaining (110 + 120 – 30 =) 200 kg at Rs. 308.32/kg.
Total cost price of the mixture = 110 × 8x + 120 × 10x = 2080x
⇒ 2080x × 1.64 = 88x + 240x + 308.32 × 200 ⇒ 2080x × 1.64 - 328x = 308.32 × 200 ⇒ 3083.2x = 308.32 × 200 ⇒ x = 20
Cost price of syrup = 8x = 160/kg.
Hence, 160.
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