Understanding Successive Discounts

The question asks us to calculate the total discount given when two successive discounts are applied to the marked price of a shirt. Rajat offers a first discount of 10 percent, followed by a second discount of 15 percent on a shirt with a marked price of Rs. 800.

Let's define the key terms involved:

• Marked Price (MP): This is the price printed on the article. In this case, the marked price of the shirt is Rs. 800.
• Discount: A reduction in the marked price of an article. Discounts are usually expressed as a percentage of the marked price.
• Successive Discounts: When a discount is applied to the marked price, and then another discount is applied to the reduced price (not the original marked price).

Calculating the Price After the First Discount

The first discount is 10 percent. This discount is calculated on the original marked price.

First Discount Amount = 10% of Marked Price

First Discount Amount = $\frac{10}{100} \times 800$

First Discount Amount = $0.10 \times 800 = 80$

So, the amount of the first discount is Rs. 80.

The price of the shirt after the first discount is the Marked Price minus the First Discount Amount.

Price after First Discount = Marked Price - First Discount Amount

Price after First Discount = $800 - 80 = 720$

The price after the first discount is Rs. 720.

Calculating the Price After the Second Discount

The second discount is 15 percent. This discount is applied to the price of the shirt after the first discount (which is Rs. 720), not the original marked price.

Second Discount Amount = 15% of Price after First Discount

Second Discount Amount = $\frac{15}{100} \times 720$

Second Discount Amount = $0.15 \times 720$

To calculate $0.15 \times 720$:

$0.15 \times 720 = \frac{15}{100} \times 720 = \frac{3 \times 5}{20 \times 5} \times 720 = \frac{3}{20} \times 720$

$\frac{3}{20} \times 720 = 3 \times \frac{720}{20} = 3 \times 36 = 108$

So, the amount of the second discount is Rs. 108.

The final selling price of the shirt is the price after the first discount minus the second discount amount.

Final Selling Price = Price after First Discount - Second Discount Amount

Final Selling Price = $720 - 108 = 612$

The final selling price of the shirt after both successive discounts is Rs. 612.

Calculating the Total Value of Discount

The question asks for the total value of the discount. The total discount is the difference between the original marked price and the final selling price.

Total Discount = Marked Price - Final Selling Price

Total Discount = $800 - 612$

Total Discount = $188$

The total value of the discount given on the shirt is Rs. 188.

Summary of Calculation Steps

The value of the discount is Rs. 188.

Revision Table: Key Concepts

Additional Information: Alternative Method for Successive Discounts

Instead of calculating the discount amounts separately, we can also calculate the selling price directly using percentage values. If a discount of $d_1$% is applied, the selling price is $(100 - d_1)$% of the previous price. If a second discount of $d_2$% is then applied, the final selling price is $(100 - d_2)$% of the price after the first discount.

For successive discounts of 10% and 15% on a marked price of Rs. 800:

Price after 10% discount = $(100 - 10)$% of MP = 90% of 800

Price after 10% discount = $0.90 \times 800 = 720$

Final Selling Price after 15% discount = $(100 - 15)$% of Price after 1st discount = 85% of 720

Final Selling Price = $0.85 \times 720$

$0.85 \times 720 = \frac{85}{100} \times 720 = \frac{17 \times 5}{20 \times 5} \times 720 = \frac{17}{20} \times 720$

$\frac{17}{20} \times 720 = 17 \times \frac{720}{20} = 17 \times 36$

$17 \times 36 = (20 - 3) \times 36 = (20 \times 36) - (3 \times 36) = 720 - 108 = 612$

Final Selling Price = Rs. 612.

Total Discount = Marked Price - Final Selling Price = $800 - 612 = 188$.

Both methods yield the same total discount value of Rs. 188.