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A shopkeeper marked the price of an article by 40% above cost price and gave discount of Rs. 224. On the final amount, he charged 10% tax. In the whole transaction, he earned Rs. 158.6. Find cost price of the article. 
  • a)
    Rs 750 
  • b)
    Rs 760 
  • c)
    Rs 744 
  • d)
    Rs 757 
  • e)
    Rs 748
Correct answer is option 'A'. Can you explain this answer?
Verified Answer
A shopkeeper marked the price of an article by 40% above cost price an...
let cost price be Rs. 100x 
Marked price = 140 /100 × 100x = Rs 140x 
Selling price = Rs (140x − 224) 
Selling price after tax = 110/100 × (140x − 224) = Rs (154x − 246.4) 
ATQ, 100x + 158.6 = 154x − 246.4 
x = 7.5 
Cost price of article = 100x = Rs 750
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Most Upvoted Answer
A shopkeeper marked the price of an article by 40% above cost price an...
Given:
- The shopkeeper marked the price of an article by 40% above the cost price.
- The shopkeeper gave a discount of Rs. 224.
- On the final amount, the shopkeeper charged a 10% tax.
- In the whole transaction, the shopkeeper earned Rs. 158.6.

To Find:
The cost price of the article.

Assumptions:
Let the cost price of the article be x.

Calculating the Selling Price:
The selling price is calculated as follows:
- Selling Price = (Cost Price + 40% of Cost Price) - Discount
- Selling Price = x + 0.4x - 224

Calculating the Final Amount:
The final amount is calculated as follows:
- Final Amount = Selling Price + 10% of Selling Price
- Final Amount = (x + 0.4x - 224) + 0.1(x + 0.4x - 224)

Calculating the Shopkeeper's Earnings:
The shopkeeper's earnings are calculated as follows:
- Earnings = Final Amount - Cost Price
- Earnings = [(x + 0.4x - 224) + 0.1(x + 0.4x - 224)] - x

Given that the Shopkeeper's Earnings are Rs. 158.6:
- 158.6 = [(x + 0.4x - 224) + 0.1(x + 0.4x - 224)] - x

Solving the Equation:
- 158.6 = 1.5x - 224 + 0.15x - 22.4 - x
- 158.6 = 0.65x - 246.4
- 0.65x = 405
- x = 405 / 0.65
- x = 630

Therefore, the cost price of the article is Rs. 630, which is not one of the given options.

Analyzing the Given Options:
Let's analyze the given options to find the closest value to the calculated cost price (Rs. 630).

- Option A: Rs. 750 (Not the correct answer)
- Option B: Rs. 760 (Not the correct answer)
- Option C: Rs. 744 (Not the correct answer)
- Option D: Rs. 757 (Not the correct answer)
- Option E: Rs. 748 (Not the correct answer)

None of the given options match the calculated cost price of Rs. 630. Therefore, the given options are incorrect.

Conclusion:
The correct answer cannot be determined from the given options.
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