The marked price of a cooker is same at four shops I, II, III ... | Mathematics MCQ | Examoogle

MathematicsArithmetic

The marked price of a cooker is same at four shops I, II, III and IV. Shop I allows two successive discounts of 12% and 79%, shop II allows successive discounts of 33% and 19%, shop III allows successive discounts of 38% and 39% and shop IV allows successive discounts of 55%, 79%, and 34% on the marked price of the cooker. Which shop is selling the cooker at the lowest price? 3373

III

Correct Answer

⚙️ TE • Technical Successive Discount AnalysisMathematicsArithmetic

Option C

Quick Summary:

Calculate the effective percentage that remains after discounts ( $100 - d$ ). The shop with the lowest resulting multiplier factor will have the lowest selling price. Focus on the largest single discount rate in each set to eliminate higher options quickly.

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📐MAMath SolutionSuccessive Discount Analysis

📋 Given

Four shops offer different sets of successive discounts on the same marked price (MP). Shop I: 12% and 79%. Shop II: 33% and 19%. Shop III: 38% and 39%. Shop IV: 55%, 79%, and 34%.

🔢 Formula Used

Effective Selling Price=MP×(1−d1100)×(1−d2100)×...\text{Effective Selling Price} = \text{MP} \times \left(1 - \frac{d_1}{100}\right) \times \left(1 - \frac{d_2}{100}\right) \times...Effective Selling Price=MP×(1−100d1​​)×(1−100d2​​)×...

⚡ Exam Hall Shortcut / Speed Trick

⚠️ Common Student Trap / Pitfall

Students often add the discount percentages directly ( $12+79=91$ ) instead of calculating successive impacts, which leads to incorrect comparisons.

📊 Diagram / Illustration

🔢 Step-by-Step Solution

Calculate Effective Multiplier for Shop I

Effective price ratio = $(1 - 0.12) \times (1 - 0.79) = 0.88 \times 0.21 = 0.1848$ .

0.88×0.21=0.18480.88 \times 0.21 = 0.18480.88×0.21=0.1848

Calculate Effective Multiplier for Shop II

Effective price ratio = $(1 - 0.33) \times (1 - 0.19) = 0.67 \times 0.81 = 0.5427$ .

0.67×0.81=0.54270.67 \times 0.81 = 0.54270.67×0.81=0.5427

Calculate Effective Multiplier for Shop III

Effective price ratio = $(1 - 0.38) \times (1 - 0.39) = 0.62 \times 0.61 = 0.3782$ .

0.62×0.61=0.37820.62 \times 0.61 = 0.37820.62×0.61=0.3782

Calculate Effective Multiplier for Shop IV

Effective price ratio = $(1 - 0.55) \times (1 - 0.79) \times (1 - 0.34) = 0.45 \times 0.21 \times 0.66 = 0.06237$ .

0.45×0.21×0.66=0.062370.45 \times 0.21 \times 0.66 = 0.062370.45×0.21×0.66=0.06237

Compare and Conclusion

Comparing $0.1848, 0.5427, 0.3782,$ and $0.06237$ , the smallest factor is $0.06237$ , corresponding to Shop IV.

0.06237<0.1848<0.3782<0.54270.06237 < 0.1848 < 0.3782 < 0.54270.06237<0.1848<0.3782<0.5427

✅

C is correct because Shop IV results in the lowest effective multiplier of 0.06237, meaning the customer pays the least compared to other shops.

Core Concepts Used

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Successive Discounts Percentage Multipliers Comparative Analysis

💡 EXAM TIP

This logic is identical to calculating compound interest depreciation where the 'amount' decreases after each successive application of the rate.

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