Question

Anupam, a trader, sells an item to Suraj at 20% discount, but he charges 10% on the discounted price for packaging and delivery. Suraj sells it for ₹ 1782 more, thereby earning a profit of 25%. At what price had the trader marked the item?

• A. ₹1620
• B. ₹7450
• C. ₹7800
• D. ₹8100

Hint:

In profit and discount problems, first calculate the cost price from profit or discount percentages, then work backward to find the marked price.

Answer 1

The Correct Option is D

Let the marked price of the item be \( x \). Step 1: Calculate the selling price from Suraj. Suraj sells the item for ₹ 1782 more than what he paid for it, and earns a 25% profit. So, Suraj's selling price is: \[ \text{Selling price of Suraj} = \text{Cost price of Suraj} + 1782. \] Since Suraj earns a 25% profit, his cost price is: \[ \text{Cost price of Suraj} = \frac{100}{125} \times \text{Selling price of Suraj}. \] Let the cost price of Suraj be \( C_s \). Then: \[ C_s = \frac{100}{125} \times (C_s + 1782). \] Solving this equation: \[ 125C_s = 100(C_s + 1782), \] \[ 125C_s = 100C_s + 178200, \] \[ 25C_s = 178200, \] \[ C_s = 7128. \] Step 2: Calculate the price Anupam sold to Suraj. The cost price of Suraj is the amount Anupam received after the 20% discount and the additional 10% charge for packaging and delivery. Hence: \[ C_s = 0.80x \times 1.10, \] \[ 7128 = 0.88x, \] \[ x = \frac{7128}{0.88} = 8100. \]