The first shopkeeper allows two successive discounts of 3% and 7%, while a second shopkeeper allows two successive discounts of 2% and 8%. A third shopkeeper allows 10% discount on the same item. From which shopkeeper should a customer buy if the marked price is the same at the three shops?
Buy from the third shopkeeper
To determine from which shopkeeper a customer should purchase, we can calculate the final selling price at each shop after the discounts are applied to find which gives the lowest price. Let's go through this step-by-step:
- The first shopkeeper offers discounts of 3% and 7% successively. The formula for successive discounts is given by:
\(D = D_1 + D_2 - \left(\frac{D_1 \cdot D_2}{100}\right)\)
- Here, \(D_1 = 3\%\) and \(D_2 = 7\%\).
- Calculate the effective discount:
\(D = 3 + 7 - \left(\frac{3 \cdot 7}{100}\right)\)
\(D = 10 - 0.21 = 9.79\%\)
- Calculate the selling price if the marked price (MP) is \(P\) for the first shopkeeper:
\(SP_1 = P \times \left(1 - \frac{9.79}{100}\right) = P \times 0.9021\)
- The second shopkeeper offers discounts of 2% and 8% successively.
- Here, \(D_1 = 2\%\) and \(D_2 = 8\%\).
- Calculate the effective discount:
\(D = 2 + 8 - \left(\frac{2 \cdot 8}{100}\right)\)
\(D = 10 - 0.16 = 9.84\%\)
- Calculate the selling price for the second shopkeeper:
\(SP_2 = P \times \left(1 - \frac{9.84}{100}\right) = P \times 0.9016\)
- The third shopkeeper offers a single discount of 10%.
- Calculate the selling price for the third shopkeeper:
\(SP_3 = P \times \left(1 - \frac{10}{100}\right) = P \times 0.90\)
- Compare the discounts and selling prices:
- First shopkeeper: \(SP_1 = P \times 0.9021\)
- Second shopkeeper: \(SP_2 = P \times 0.9016\)
- Third shopkeeper: \(SP_3 = P \times 0.90\)
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Important Questions from Discount and MP
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