Kunal bought an article and sold it at a loss of 15%. If he had bought it for 18% less and sold it for ₹108 more, then he would have had a profit of 30%. Find the cost price of the article.

Given:

Loss on selling the article = 15%

Discount on purchase = 18%

Increase in selling price = ₹108

Profit if sold at increased price = 30%

Concept:

Cost price, selling price, loss, and profit are related by the formulas:

Selling Price = Cost Price - Loss (or + Profit)

Calculation:

Let's denote the original cost price of the article as 'C'.

The selling price with a 15% loss = C - 15% of C = 0.85C.

If Kunal had bought it for 18% less, the cost price =  C - 18% of C = 0.82C.

If he had sold it for ₹108 more, the selling price = 0.85C + ₹108.

Given that this new selling price would have given a profit of 30%,

we can set up an equation: 0.82C + 30% of 0.82C = 0.85C + ₹108.

⇒ 1.3 × 0.82C = 0.85C + ₹108.

⇒ C = ₹108 / (1.3 × 0.82 - 0.85) = ₹500.

Therefore, the cost price of the article is approximately ₹500.
 Alternate Method

Let CP = 1000

Loss = 15%

so

SP = 85% of 1000 = 850

Now new CP = 82% of 1000 = 820

Profit% = 30%

So

New SP = 130% of 820 = 1066

so

New SP - SP = 1066 - 850 = 216 = rs. 108

so

1 = Rs. 0.5

So

CP = 1000 = Rs. 1000 × 0.5 = Rs. 500