A shopkeeper allows a 4% discount on his marked price. If the cost price of an article is ₹120 and he has to m

Question

A shopkeeper allows a 4% discount on his marked price. If the cost price of an article is ₹120 and he has to make a profit of 10%, then his marked price must be:

Examoogle · Accepted Answer

The correct answer is Option D: ₹137.50. Calculate the Selling Price (SP) first: 10% of 120 is 12, so SP = 132. Then, since 96% of Marked Price is 132, use 132 / 0.96 = 137.5.

Step-by-Step Solution & Concepts:
Shortcut Trick: Calculate the Selling Price (SP) first: 10% of 120 is 12, so SP = 132. Then, since 96% of Marked Price is 132, use 132 / 0.96 = 137.5.

Formula Used: $$MP = \frac{CP 	imes (100 + 	ext{Profit}\%)}{100 - 	ext{Discount}\%}$$

Given: Cost Price (CP) = ₹120, Profit Percentage = 10%, Discount = 4%

Steps: Calculate Selling Price: To achieve a profit of 10% on a cost price of ₹120, calculate the selling price as $SP = CP 	imes (1 + \frac{10}{100}) = 120 	imes 1.10 = 132$.. Define Relation between MP and SP: The shopkeeper allows a 4% discount on the marked price (MP), meaning $SP = MP 	imes (1 - \frac{4}{100}) = MP 	imes 0.96$.. Solve for Marked Price: Equate the expressions for SP: $132 = MP 	imes 0.96$. Dividing both sides gives $MP = \frac{132}{0.96} = 137.50$.

Answer: D is correct because the required marked price is calculated to be ₹137.50 to ensure a 10% profit after a 4% discount.

Exam Tip: This concept is identical to solving 'successive percentage' problems in exams; always compute the actual transaction value (SP) first.

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