CAT 2025Slot 3QAQuestion & Solution
Question
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 the 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. 138825, then the marked price per unit, in rupees, was
Options
520
525
510
515
Solution
1. Concept Used
- Topic: Profit and Loss — Marked Price, Discount, Revenue and Cost
- Formula: $$\text{Profit} = \text{Total Revenue} - \text{Total Cost}$$
2. Calculation
Let the marked price per unit be $$X$$.
Step 1: Find the Selling Price per unit in each month.
In January, a discount of 20% is given, so the selling price $$= 0.80X$$.
In February, a discount of 10% is given, so the selling price $$= 0.90X$$.
In March, a discount of 5% is given, so the selling price $$= 0.95X$$.
In April, no discount is given, so the selling price $$= X$$.
Step 2: Calculate Total Revenue.
Units sold were 120, 135, 150, and 165 in January, February, March, and April respectively.
$$\text{Total Revenue} = 120 \times 0.80X + 135 \times 0.90X + 150 \times 0.95X + 165 \times X$$
$$= 96X + 121.5X + 142.5X + 165X$$
$$= 525X$$
Step 3: Calculate Total Cost.
Total units sold $$= 120 + 135 + 150 + 165 = 570$$
Cost price per unit $$= \text{Rs. } 240$$
$$\text{Total Cost} = 570 \times 240 = \text{Rs. } 136800$$
Step 4: Apply the Profit Formula.
$$\text{Profit} = \text{Total Revenue} - \text{Total Cost}$$
$$138825 = 525X - 136800$$
$$525X = 138825 + 136800 = 275625$$
$$X = \frac{275625}{525} = 525$$
3. Solution
Answer = Option B ✅
The marked price per unit is Rs. 525.