A shopkeeper marked the price of an article by 40\% above cost price and gave a discount of Rs. 224. On the final amount after discount, he charged 10\% tax. In the whole transaction, he earned Rs. 158.6. Find the cost price of the article.

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Accepted Answer

**Solution:**

1. Let the cost price be Rs. $100x$.

2. Marked price is 40\% above cost price:
   $$
   \text{Marked Price} = 100x + 40\% \times 100x = 140x
   $$

3. Discount given is Rs. 224, so selling price before tax:
   $$
   \text{Selling Price} = 140x - 224
   $$

4. Tax of 10\% is charged on the selling price:
   $$
   \text{Selling Price after tax} = (140x - 224) + 10\% \times (140x - 224) = 1.1 \times (140x - 224) = 154x - 246.4
   $$

5. The shopkeeper earned Rs. 158.6 profit on cost price, so:
   $$
   \text{Cost Price} + \text{Profit} = \text{Selling Price after tax} \
   100x + 158.6 = 154x - 246.4
   $$

6. Solve for $x$:
   $$
   158.6 + 246.4 = 154x - 100x \
   405 = 54x \
   x = \frac{405}{54} = 7.5
   $$

7. Therefore, cost price:
   $$
   100x = 100 \times 7.5 = \text{Rs. } 750
   $$

**Answer:** Rs. 750

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