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

Approach: Work in profit-per-unit terms by guessing from the options (CAT-smart back-solving). The numbers are clean, so plug $M=525$ from the options straight into total revenue and check the profit lands on Rs. $1{,}38{,}825$.

Step 1: Revenue multiplier. The discounted unit prices for $M=525$ are: Jan $0.8\times525=420$, Feb $0.9\times525=472.5$, Mar $0.95\times525=498.75$, Apr $525.$

Step 2: Month-wise revenue.
Jan: $120\times420 = 50{,}400$
Feb: $135\times472.5 = 63{,}787.5$
Mar: $150\times498.75 = 74{,}812.5$
Apr: $165\times525 = 86{,}625$
Total revenue $= 50{,}400+63{,}787.5+74{,}812.5+86{,}625 = 2{,}75{,}625.$

Step 3: Subtract cost. Cost $= 570\times240 = 1{,}36{,}800.$
Profit $= 2{,}75{,}625 - 1{,}36{,}800 = 1{,}38{,}825.$ This is exactly the given profit, so $M=525$ is confirmed.

(Other options fail: e.g. $M=520$ gives revenue $520\times525 = 2{,}73{,}000$ and profit $1{,}36{,}200 \ne 1{,}38{,}825.$)

\[ \text{Marked price} = \text{Rs. } 525 \]