The marked price of a cooker is same at four shops I, II, III and IV. Shop I allows two successive discounts o

Question

The marked price of a cooker is same at four shops I, II, III and IV. Shop I allows two successive discounts of 23% and 92%, shop II allows successive discounts of 88% and 47%, shop III allows successive discounts of 11% and 28% and shop IV allows successive discounts of 63%, 76% and 86% on the marked price of the cooker. Which shop is selling the cooker at the lowest price? 3370

Examoogle · Accepted Answer

The correct answer is Option B: IV. Calculate the multiplier $(1 - \frac{d}{100})$ for each discount. The shop with the smallest product of these multipliers offers the lowest selling price.

Step-by-Step Solution & Concepts:
Shortcut Trick: Calculate the multiplier $(1 - \frac{d}{100})$ for each discount. The shop with the smallest product of these multipliers offers the lowest selling price.

Formula Used: $$	ext{Selling Price} = 	ext{Marked Price} 	imes \prod_{i=1}^{n} (1 - \frac{d_i}{100})$$

Given: Marked price is constant for all shops. Shop I: 23% and 92% discounts. Shop II: 88% and 47% discounts. Shop III: 11% and 28% discounts. Shop IV: 63%, 76% and 86% discounts.

Steps: Calculate Shop I multiplier: Successive discounts of 23% and 92% result in multipliers $(1 - 0.23) = 0.77$ and $(1 - 0.92) = 0.08$. The product is:. Calculate Shop II multiplier: Successive discounts of 88% and 47% result in multipliers $(1 - 0.88) = 0.12$ and $(1 - 0.47) = 0.53$. The product is:. Calculate Shop III multiplier: Successive discounts of 11% and 28% result in multipliers $(1 - 0.11) = 0.89$ and $(1 - 0.28) = 0.72$. The product is:. Calculate Shop IV multiplier: Successive discounts of 63%, 76% and 86% result in multipliers $(1 - 0.63) = 0.37$, $(1 - 0.76) = 0.24$, and $(1 - 0.86) = 0.14$. The product is:. Compare results: Comparing the resulting values: $0.0616$, $0.0636$, $0.6408$, and $0.012432$. The smallest value is $0.012432$, which corresponds to Shop IV.

Answer: B is correct because the product of the remaining price fractions for Shop IV is 0.012432, which is the lowest value among all shops.

Exam Tip: This concept is identical to compound interest calculations where you multiply the growth factors $(1 + r/100)$. In discounts, we use decay factors $(1 - r/100)$.

Examoogle · Answer

Option A: III

Examoogle · Answer

Option C: II

Examoogle · Answer

Option D: I Question ID : 441009536895 Option 1 ID : 4410092102977 Option 2 ID : 4410092102976 Option 3 ID : 4410092102978 Option 4 ID : 4410092102979 Status : Answered Chosen Option : B

Correct Answer

Solve 10,000+ More Questions with AI Tutor

Discussion (0)

Correct Answer

Solve 10,000+ More Questions with AI Tutor

Related Questions

Discussion (0)