The shopkeeper offers two successive discounts on a machine that is marked at ₹18,000 so that its selling pric

Question

The shopkeeper offers two successive discounts on a machine that is marked at ₹18,000 so that its selling price gets reduced to ₹12,960. If 10% and $x\%$ are the respective discounts, the value of $x$ is:

Examoogle · Accepted Answer

The correct answer is Option A: 20. Finding Second Discount Rate x% with Marked Price ₹18,000 and SP ₹12,960

Step-by-Step Solution & Concepts:
Key Fact: Finding Second Discount Rate x% with Marked Price ₹18,000 and SP ₹12,960

Given: Marked price $MP = ₹18,000$; Selling price $SP = ₹12,960$; First discount $= 10\%$

Key Formulas: $SP = MP 	imes \left(1 - \frac{d_1}{100}ight) 	imes \left(1 - \frac{x}{100}ight)$

Key Points: $18000 	imes 0.90 	imes 0.80 = 12960$.; Value of $x$ is 20.

Steps: Calculate Intermediate Price After 10% Discount: $$	ext{Price}_1 = 18000 	imes (1 - 0.10) = 18000 	imes 0.90 = ₹16,200$$. Calculate Second Discount x%: The additional discount amount is: $$	ext{Discount}_2 = 16200 - 12960 = ₹3,240$$ $$x = \frac{3240}{16200} 	imes 100 = \frac{324}{1620} 	imes 100 = 20\%$$

Answer: Option A is correct — 20

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