Profit and Loss Question 1 - CAT 2025
The monthly sales of a product from January to April were 120, 135, 150, and 165 units, respectively. The cost price of the product was Rs. 240 per unit, and a fixed marked price was used for the product in all four months. Discounts of 20%, 10%, and 5% were given on the marked price per unit in January, February, and March, respectively, while no discounts were given in April. If the total profit from January to April was Rs. 138,825, then the marked price per unit, in rupees, was:
Step-by-Step Explanation
- Total Units Sold: 120 + 135 + 150 + 165 = 570 units.
- Total Cost Price (CP): 570 × 240 = Rs. 136,800.
- Total Revenue Required: Total CP + Total Profit = 136,800 + 138,825 = Rs. 275,625.
Let the marked price per unit be X.
The selling price (SP) for each month can be expressed in terms of X after applying the respective discounts:
- January SP: 0.80X
- February SP: 0.90X
- March SP: 0.95X
- April SP: 1.00X
Now, set up the total revenue equation:
Revenue = 120 × 0.80X + 135 × 0.90X + 150 × 0.95X + 165 × 1.00X
275,625 = 96X + 121.5X + 142.5X + 165X
275,625 = 525X
X = 275,625 / 525 = 525
The marked price per unit was Rs. 525.
Correct Option: B
💡 FundaMakers Tip:
When dealing with multiple intervals or months with a constant baseline value (like Marked Price X), do not calculate the profit of each month individually. Instead, pool the total revenue together as a single algebraic expression in terms of X and equate it to the Total CP + Total Profit. This avoids repetitive calculations and saves precious time.