A shopkeeper sells an article at a 20% profit. If he had bought it at 10% less and sold it for ₹18 less, he would have gained 25%. Find the cost price of the article.

Question

Accepted Answer

Let's solve this classic profit and loss word problem using algebra.

### Step-by-Step Solution:
1. Let the original Cost Price (CP) of the article be $₹x$.
2. Original Selling Price (SP) at 20% profit:
   $$	ext{SP}_1 = x + 0.20x = 1.20x$$
3. New Cost Price ($	ext{CP}_2$) if bought at 10% less:
   $$	ext{CP}_2 = x - 0.10x = 0.90x$$
4. New Selling Price ($	ext{SP}_2$) with a 25% profit on the new CP:
   $$	ext{SP}_2 = 	ext{CP}_2 	imes (1 + 0.25) = 0.90x 	imes 1.25 = 1.125x$$
5. According to the problem, the new SP is ₹18 less than the original SP:
   $$	ext{SP}_1 - 	ext{SP}_2 = 18$$
   $$1.20x - 1.125x = 18$$
   $$0.075x = 18$$
   $$x = \frac{18}{0.075} = \frac{18000}{75} = 240$$

**Answer:** The original cost price of the article is **₹240**.

A shopkeeper sells an article at a 20% profit. If he had bought it at 10% less and sold it for ₹18 less, he would have gained 25%. Find the cost price of the article. - DDCET Q&A

A shopkeeper sells an article at a 20% profit. If he had bought it at 10% less and sold it for ₹18 less, he would have gained 25%. Find the cost price of the article.

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