Profit and Loss Question 1 - CAT 2022
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:
Step-by-Step Explanation
- Set up the Cost Price (CP):
Let the cost price of juice be Rs. 10x per kg.
Since syrup is 20% less costly than juice, the cost price of syrup = Rs. 8x per kg.
- Calculate Total Cost Price:
Total CP = 110 kg × 8x + 120 kg × 10x = 880x + 1200x = 2080x
- Break down the Selling Price (SP):
- 10 kg of syrup sold at 10% profit:
SP₁ = 10 × 8x × 1.10 = 88x
- 20 kg of juice sold at 20% profit:
SP₂ = 20 × 10x × 1.20 = 240x
- Remaining mixture:
The remaining quantities are 110 − 10 = 100 kg of syrup and 120 − 20 = 100 kg of juice.
Total mixture weight = 100 + 100 = 200 kg
This mixture is sold at ₹ 308.32 per kg.
SP₃ = 200 × 308.32 = ₹ 61,664
- Formulate the Overall Profit Equation:
The total selling price is the sum of all three parts, which reflects an overall profit of 64% on the total CP:
Total SP = 1.64 × Total CP
88x + 240x + 61,664 = 1.64 × 2080x
328x + 61,664 = 3411.2x
61,664 = 3411.2x − 328x
61,664 = 3083.2x
x = 61,664 / 3083.2 = 20
- Find the Cost Price of Syrup:
CP of syrup = 8x = 8 × 20 = ₹ 160
Correct Answer: 160
💡 FundaMakers Tip:
Don't let ugly decimals like ₹ 308.32 scare you mid-exam! CAT test-setters choose these precise values intentionally so that they simplify perfectly at the very last step. Notice how 3083.2 × 2 = 6166.4, meaning x effortlessly simplifies to 20.
Whenever you encounter complex mixtures mixed with component-wise profits, maintain a neat bookkeeping ledger: Total CP vs. Total SP. Keeping variables clustered cleanly prevents arithmetic errors when the final linear equation is evaluated.