Understanding the Discount Problem
This problem involves calculating a second successive discount. We are given the initial marked price of an item (a table), the percentage of the first discount, and the final price the customer paid after two discounts. Our goal is to find the percentage of the second discount.
Key Information Provided:
- Marked Price (MP): ₹1,400
- First Discount (D1): 12%
- Final Selling Price (SP): ₹1,133.44
- Second Discount (D2): To be calculated
Step-by-Step Calculation of the Second Discount
Step 1: Calculate the price after the first discount
The first discount is 12% on the marked price of ₹1,400. We can calculate the price after this discount (let's call it Price 1) using the formula:
Price 1 = MP \times (1 - \frac{D1}{100})
Substituting the values:
Price 1 = 1400 \times (1 - \frac{12}{100})
Price 1 = 1400 \times (1 - 0.12)
Price 1 = 1400 \times 0.88
Price 1 = 1232
So, after the first 12% discount, the price of the table becomes ₹1,232.
Step 2: Calculate the amount of the second discount
The customer paid ₹1,133.44 for the table. This final price was reached after applying the second discount to Price 1 (₹1,232). The amount of the second discount is the difference between Price 1 and the final Selling Price (SP).
Second Discount Amount = Price 1 - SP
Second Discount Amount = 1232 - 1133.44
Second Discount Amount = 98.56
The value of the second discount is ₹98.56.
Step 3: Calculate the second discount percentage
The second discount percentage (D2) is calculated based on the price at which the second discount was applied, which is Price 1 (₹1,232). The formula is:
D2 = (\frac{Second Discount Amount}{Price 1}) \times 100
Substituting the values:
D2 = (\frac{98.56}{1232}) \times 100
D2 = 0.08 \times 100
D2 = 8
Therefore, the second discount percentage offered was 8%.
Conclusion
By applying a 12% discount and then an 8% discount successively to the marked price of ₹1,400, the final selling price comes down to ₹1,133.44. The calculation confirms that the second discount percentage is 8%.
Important Questions from Discount and MP
- Two successive discounts of 25% and 10% on a deal are equivalent to a single discount of:
- A shopkeeper offers the following three schemes. Which scheme has the maximum discount percent?
I. Two successive discounts of 15% and 20%.
II. Buy 4 get 2 free.
III. Buy 6 get 4 free - A shopkeeper is given a 10% trade discount and a 5% scheme discount (free units). On purchasing 100 units priced at ₹50 each, what is the trade discount amount?
- What is the equivalent single discount for successive discounts of 20% and 10%?
- Rahul buys a box of pens (listed price of ₹900) with a trade discount of 30%. What is the net price?
