Understanding Successive Discounts on a Shirt

The problem asks us to find the total reduction in price when a shirt, initially marked at ₹1,200, is sold after applying two successive discounts: 5% and then 15%. We need to calculate the difference between the marked price and the final selling price.

Calculating the Selling Price After Discounts

To find the final selling price (SP), we apply the discounts one after the other. The second discount is applied to the price calculated after the first discount, not the original marked price.

Step 1: Calculate the price after the first discount (5%)

Marked Price (MP) = ₹1,200

First Discount = 5%

Discount amount = $5\% \text{ of } ₹1,200 = \frac{5}{100} \times 1200 = ₹60$

Price after first discount = Marked Price - First Discount Amount

Price after first discount = $1200 - 60 = ₹1140$

Step 2: Calculate the price after the second discount (15%)

The second discount of 15% is applied to the price calculated in Step 1, which is ₹1140.

Second Discount = 15%

Second Discount amount = $15\% \text{ of } ₹1140 = \frac{15}{100} \times 1140$

Second Discount amount = $0.15 \times 1140 = ₹171$

Final Selling Price (SP) = Price after first discount - Second Discount Amount

SP = $1140 - 171 = ₹969$

Alternative Method: Using Discount Multipliers

We can also calculate the selling price directly:

SP = Marked Price $\times (1 - \frac{\text{Discount}_1}{100}) \times (1 - \frac{\text{Discount}_2}{100})$

SP = $1200 \times (1 - \frac{5}{100}) \times (1 - \frac{15}{100})$

SP = $1200 \times (\frac{100 - 5}{100}) \times (\frac{100 - 15}{100})$

SP = $1200 \times (\frac{95}{100}) \times (\frac{85}{100})$

SP = $1200 \times 0.95 \times 0.85$

SP = $1140 \times 0.85$

SP = $969$

Calculating the Difference Between Marked Price and Selling Price

The question asks by how many rupees the selling price is less than the marked price. This is the total discount amount.

Difference = Marked Price - Selling Price

Difference = $1200 - 969$

Difference = ₹231

Summary of Calculation

Therefore, the selling price is ₹231 less than the marked price.