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
| Marked Price (MP) | ₹1,200 |
| First Discount (5%) | ₹60 |
| Price after 1st Discount | ₹1,140 |
| Second Discount (15% on ₹1,140) | ₹171 |
| Final Selling Price (SP) | ₹969 |
| Difference (MP - SP) | ₹231 |
Therefore, the selling price is ₹231 less than the marked price.
Important Questions from Percentage
Radha saves 25% of her income. If her expenditure increases by 20% and her income increases by 29%, then her savings increase by;
The income of A is 45% more than the income of B and the income of C is 60% less than the sum of the incomes of A and B. The income of D is 20% more than that of C. If the difference between the incomes of B and D is Rs. 13200, then the income (in Rs.) of C is:
The price of cooking oil increased by 25%. Find by how much percentage a family must reduce its consumption in order to maintain the same budget.
The population of a city increased by 30% in the first year and decreased by 15% in the next year. If the present population is 11,050 then population 2 years ago was:
The income of A is 30% less than the income of B and the income of B is 137.5% more than that of C. If the income of A is Rs. 28500 less than that of B, then the income (in Rs.) of C is:
