The marked price of a cooker is same at four shops I, II, III and IV. Shop I allows two successive discounts of 80% and 44%, shop II allows successive discounts of 58% and 62%, shop III allows successive discounts of 67% and 85%, and shop IV allows successive discounts of 41%, 91%, and 74% on the marked price of the cooker. Which shop is selling the cooker at the lowest price?
IV
For successive discounts, the final selling price as a fraction of the marked price is the product of the remaining fractions after each discount, so a lower product means a lower selling price.
Shop I: (1 - 0.80)(1 - 0.44) = 0.20 x 0.56 = 0.112. Shop II: (1 - 0.58)(1 - 0.62) = 0.42 x 0.38 = 0.1596. Shop III: (1 - 0.67)(1 - 0.85) = 0.33 x 0.15 = 0.0495.
Shop IV: (1 - 0.41)(1 - 0.91)(1 - 0.74) = 0.59 x 0.09 x 0.26 = 0.0138 (approx), which is the smallest fraction of the marked price among all shops.
Hence, the correct answer is shop IV.
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Important Questions from Successive Selling
By selling a watch at Rs. 840 a person loses 4%. Find the gain or loss if he sold it for Rs. 875?
Gaurav bought some articles at 5 for Rs. 6 and sold them at 10 for Rs. 11. His loss percentage is:
The increase in the price of a certain item was 25%. Then the price was decreased by 20% and then again increased by 10%. What is the resultant increase in the price?
- The selling price of 24 articles is equal to the cost price of 26 articles. If, due to a change in market conditions, the selling price of each article decreases by $10\%$ and the cost price of each article increases by $5\%$, what will be the new gain or loss percentage (correct to two decimal places)?
X sells goods to Y at a profit of 20 percent and Y sells the same goods to Z at a profit of 50 percent. If the cost price for Z is Rs 9000, then what is the cost of the goods for X?
