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

• A. \(525\)
• B. \(510\)
• C. \(520\)
• D. \(515\)

Hint:

In profit and loss problems over multiple periods:
Keep the marked price as a single variable \(M\).
Express each month's profit as \((\text{SP} - \text{CP}) \times \text{quantity}\).
Add all monthly profits and equate to the given total profit. The coefficients usually simplify nicely.

Answer 1

The Correct Option is A

Let the marked price per unit be \(M\) rupees. Cost price per unit is Rs. \(240\).
Step 1: Compute selling price and profit per unit for each month.
January: Discount \(= 20%\) Selling price \(= 0.8M\) Profit per unit \(= 0.8M - 240\) Units sold \(= 120\) \[ \text{Profit in Jan} = 120(0.8M - 240) \]
February: Discount \(= 10%\) Selling price \(= 0.9M\) Profit per unit \(= 0.9M - 240\) Units sold \(= 135\) \[ \text{Profit in Feb} = 135(0.9M - 240) \]
March: Discount \(= 5%\) Selling price \(= 0.95M\) Profit per unit \(= 0.95M - 240\) Units sold \(= 150\) \[ \text{Profit in Mar} = 150(0.95M - 240) \]
April: No discount Selling price \(= M\) Profit per unit \(= M - 240\) Units sold \(= 165\) \[ \text{Profit in Apr} = 165(M - 240) \]
Step 2: Use total profit to form the equation. Total profit: \[ 120(0.8M - 240) + 135(0.9M - 240) + 150(0.95M - 240) + 165(M - 240) = 138825. \] Simplify each term: \[ 120 \cdot 0.8M = 96M,\quad 135 \cdot 0.9M = 121.5M,\quad 150 \cdot 0.95M = 142.5M,\quad 165M. \] Sum of coefficients of \(M\): \[ 96M + 121.5M + 142.5M + 165M = 525M. \] Constant terms: \[ 120(-240) + 135(-240) + 150(-240) + 165(-240) = -240(120 + 135 + 150 + 165) = -240 \cdot 570 = -136800. \] So the equation becomes: \[ 525M - 136800 = 138825. \] \[ 525M = 138825 + 136800 = 275625 \quad \Rightarrow \quad M = \frac{275625}{525} = 525. \] Hence, the marked price per unit is: \[ \boxed{525}. \]