Understanding Successive Discounts

This problem involves calculating the final selling price and the total discount offered by different shopkeepers who apply successive discounts on the same marked article. Successive discounts mean that the second discount is applied to the price after the first discount has been deducted.

The marked price of the article is Rs. 4820 for all three shopkeepers.

Calculating Discount for Shopkeeper A

Shopkeeper A offers successive discounts of 20% and 20%.

Let the marked price be MP. The price after the first discount of 20% is:

Price after 1st discount = \(MP \times \left(1 - \frac{20}{100}\right)\)

Price after 1st discount = \(4820 \times \left(\frac{80}{100}\right) = 4820 \times 0.80 = 3856\)

Now, the second discount of 20% is applied to this new price (Rs. 3856).

Selling Price (SP) for A = \(3856 \times \left(1 - \frac{20}{100}\right)\)

SP for A = \(3856 \times \left(\frac{80}{100}\right) = 3856 \times 0.80 = 3084.80\)

The total discount given by shopkeeper A is the difference between the marked price and the selling price.

Discount for A = Marked Price - Selling Price for A

Discount for A = \(4820 - 3084.80 = 1735.20\)

Calculating Discount for Shopkeeper B

Shopkeeper B offers successive discounts of 25% and 15%.

Price after the first discount of 25%:

Price after 1st discount = \(4820 \times \left(1 - \frac{25}{100}\right)\)

Price after 1st discount = \(4820 \times \left(\frac{75}{100}\right) = 4820 \times 0.75 = 3615\)

Now, the second discount of 15% is applied to Rs. 3615.

Selling Price (SP) for B = \(3615 \times \left(1 - \frac{15}{100}\right)\)

SP for B = \(3615 \times \left(\frac{85}{100}\right) = 3615 \times 0.85 = 3072.75\)

The total discount given by shopkeeper B is:

Discount for B = Marked Price - Selling Price for B

Discount for B = \(4820 - 3072.75 = 1747.25\)

Calculating Discount for Shopkeeper C

Shopkeeper C offers successive discounts of 30% and 10%.

Price after the first discount of 30%:

Price after 1st discount = \(4820 \times \left(1 - \frac{30}{100}\right)\)

Price after 1st discount = \(4820 \times \left(\frac{70}{100}\right) = 4820 \times 0.70 = 3374\)

Now, the second discount of 10% is applied to Rs. 3374.

Selling Price (SP) for C = \(3374 \times \left(1 - \frac{10}{100}\right)\)

SP for C = \(3374 \times \left(\frac{90}{100}\right) = 3374 \times 0.90 = 3036.60\)

The total discount given by shopkeeper C is:

Discount for C = Marked Price - Selling Price for C

Discount for C = \(4820 - 3036.60 = 1783.40\)

Comparing Discounts Offered

Let's compare the total discounts offered by each shopkeeper:

From the table, we can see that Shopkeeper C gives the maximum discount, which is Rs. 1783.40.

Maximum Discount Conclusion

Shopkeeper C provides the highest discount of Rs. 1783.40 on the article marked at Rs. 4820.

Revision Table: Key Concepts

Additional Information: Effective Single Discount

Two successive discounts of \(d_1\%\) and \(d_2\%\) are equivalent to a single discount. The formula for the equivalent single discount (D) is:

\(D = d_1 + d_2 - \frac{d_1 \times d_2}{100}\)

Let's check this formula for the given cases:

• Shopkeeper A (20% and 20%): \(D = 20 + 20 - \frac{20 \times 20}{100} = 40 - \frac{400}{100} = 40 - 4 = 36\%\)
• Shopkeeper B (25% and 15%): \(D = 25 + 15 - \frac{25 \times 15}{100} = 40 - \frac{375}{100} = 40 - 3.75 = 36.25\%\)
• Shopkeeper C (30% and 10%): \(D = 30 + 10 - \frac{30 \times 10}{100} = 40 - \frac{300}{100} = 40 - 3 = 37\%\)

The shopkeeper offering the highest effective single discount will give the maximum total discount in Rupees, assuming the marked price is the same. In this case, 37% (Shopkeeper C) is the highest effective discount percentage, which aligns with our finding that Shopkeeper C gives the maximum discount amount.

Note that the order of successive discounts does not matter when calculating the final price or the total discount.