A product was marked for sale with a label price, which is at 20% discount on the printed price. At the time of sale, the shopkeeper gave an additional 10% discount on the label price. If a customer bought the product at Rs. 468, then what is the printed price of the product?
Rs. 650
Calculating the Printed Price with Multiple Discounts
Let's break down this problem involving discounts on a product to find its original printed price. We are given the final selling price after two consecutive discounts: first on the printed price to get the label price, and then another on the label price to get the final selling price.
Understanding the Pricing Terms
- Printed Price: This is the initial price marked on the product before any discounts. This is what we need to find.
- Label Price: This is the price after the first discount is applied to the printed price.
- Selling Price: This is the final price the customer pays after all discounts are applied to the label price.
Step-by-Step Calculation
Let \(P\) be the Printed Price (in Rs.).
Step 1: Calculate the Label Price
The label price is at a 20% discount on the printed price. This means the label price is \(100\% - 20\% = 80\%\) of the printed price.
Label Price \(L = P - 20\%\) of \(P\)
In terms of calculation:
\(L = P - 0.20 \times P\)
\(L = (1 - 0.20) \times P\)
\(L = 0.80 \times P\)
Step 2: Calculate the Selling Price from the Label Price
The shopkeeper gave an additional 10% discount on the label price at the time of sale. This means the selling price is \(100\% - 10\% = 90\%\) of the label price.
Selling Price \(S = L - 10\%\) of \(L\)
In terms of calculation:
\(S = L - 0.10 \times L\)
\(S = (1 - 0.10) \times L\)
\(S = 0.90 \times L\)
Step 3: Use the Given Selling Price to Find the Label Price
We are given that the customer bought the product at Rs. 468. So, \(S = 468\).
Substitute this into the equation from Step 2:
\(468 = 0.90 \times L\)
Now, solve for \(L\):
\(L = \frac{468}{0.90}\)
\(L = \frac{468}{\frac{90}{100}}\)
\(L = \frac{468 \times 100}{90}\)
\(L = \frac{46800}{90}\)
\(L = 520\)
So, the Label Price was Rs. 520.
Step 4: Use the Label Price to Find the Printed Price
Now we use the equation from Step 1:
\(L = 0.80 \times P\)
Substitute the calculated value of \(L = 520\):
\(520 = 0.80 \times P\)
Now, solve for \(P\):
\(P = \frac{520}{0.80}\)
\(P = \frac{520}{\frac{80}{100}}\)
\(P = \frac{520 \times 100}{80}\)
\(P = \frac{52000}{80}\)
\(P = 650\)
So, the Printed Price of the product is Rs. 650.
Summary of Prices
| Price Type | Calculation/Value |
|---|---|
| Printed Price | Rs. 650 |
| 20% Discount on Printed Price | \(0.20 \times 650 = 130\) |
| Label Price | \(650 - 130 = 520\) |
| 10% Discount on Label Price | \(0.10 \times 520 = 52\) |
| Selling Price | \(520 - 52 = 468\) |
The calculated selling price (Rs. 468) matches the given selling price, confirming our steps are correct.
Therefore, the printed price of the product is Rs. 650.
Revision Table: Key Concepts
| Concept | Explanation | Formula/Relationship |
|---|---|---|
| Discount | A reduction in price. Usually expressed as a percentage of the original price. | Discount Amount = Discount Rate \(\times\) Original Price |
| Selling Price after Discount | The price after the discount is subtracted from the original price. | Selling Price = Original Price - Discount Amount Selling Price = Original Price \(\times\) (1 - Discount Rate) |
| Consecutive Discounts | Applying one discount after another on the successively reduced price. The second discount is applied to the price after the first discount. | Not simply adding the discount percentages. Each discount is applied to a different base price. |
Additional Information: Successive Discounts
It is important to note that two successive discounts of 20% and 10% are not equivalent to a single discount of \(20\% + 10\% = 30\%\). This is because the second discount is applied to a smaller base (the label price), not the original printed price.
Let's verify this with an example:
If the printed price was Rs. 100:
- Single 30% discount: Selling price = \(100 - 0.30 \times 100 = 100 - 30 = 70\)
- Successive 20% and 10% discounts:
- Price after 20% discount (Label Price) = \(100 - 0.20 \times 100 = 80\)
- Price after additional 10% discount (Selling Price) = \(80 - 0.10 \times 80 = 80 - 8 = 72\)
As you can see, Rs. 70 is different from Rs. 72. The effective single discount equivalent to successive discounts of \(d_1\%\) and \(d_2\%\) is given by the formula:
\(Effective Discount = (d_1 + d_2 - \frac{d_1 \times d_2}{100})\%\)
For 20% and 10%:
\(Effective Discount = (20 + 10 - \frac{20 \times 10}{100})\%\)
\(Effective Discount = (30 - \frac{200}{100})\%\)
\(Effective Discount = (30 - 2)\%\)
\(Effective Discount = 28\%\)
This means the customer effectively received a 28% discount on the original printed price. Let's check this: 28% of Rs. 650 is \(0.28 \times 650 = 182\). Selling Price = \(650 - 182 = 468\), which matches the given selling price.
Important Questions from Quant Based Puzzle
Three years ago, the difference between the age of Ravish and the age of Kailash was 18 years. Three years from today, Ravish will be three times as old as Kailash. What is the present age of Ravish (in years)?
Seven years from now, Anamika will be as old as Malini was 4 years ago. Srinidhi was born 2 years ago. The average age of Anamika, Malini and Srinidhi 10 years from now will be 33 years. What is the present age of Anamika?
An amount of ₹1,003 is to be distributed among A, B and C in the ratio of 11 : 23 : 25. How many rupees would B get more than A?
In an exam of 80 questions, a correct answer gives 1 marks but a wrong answer deducts 1 marks, and if a question in not attempted there is no deduction in marks. If a student attempted only 80% of the question and got 32 marks, then how many questions did he answer correctly?
The ratio of the present ages of Asha and Lata is 5 : 6. If the difference between their ages is 6 years, then what will be Lata’s age after 5 years?
