Calculate Equivalent Discount for Successive Discounts
This question requires finding a single discount percentage that is equal to applying two consecutive discounts, 5% and 20%. We can solve this using a hypothetical marked price or a direct formula.
Method 1: Using Hypothetical Marked Price
- Assume the Marked Price (MP) is $100.
-
Calculate the price after the first discount of 5%.
Price after 1st discount = MP - (5% of MP)
Price = $100 - ( \frac{5}{100} \times 100 ) = 100 - 5 = 95$
-
Calculate the price after the second discount of 20% on the intermediate price ($95$).
Price after 2nd discount = $95 - (20\% \text{ of } 95)$
Price = $95 - ( \frac{20}{100} \times 95 ) = 95 - (0.20 \times 95) = 95 - 19 = 76$
-
Calculate the total discount amount.
Total Discount = Marked Price - Final Price
Total Discount = $100 - 76 = 24$
-
Calculate the equivalent single discount percentage.
Equivalent Discount = $ \frac{\text{Total Discount}}{\text{Marked Price}} \times 100\% $
Equivalent Discount = $ \frac{24}{100} \times 100\% = 24\% $
Method 2: Using the Discount Formula
For two successive discounts, $d_1$ and $d_2$, the equivalent single discount ($D$) can be calculated using the formula:
$ D = d_1 + d_2 - \frac{d_1 \times d_2}{100} $
Given $d_1 = 5\%$ and $d_2 = 20\%$.
-
Substitute the values into the formula:
$ D = 5 + 20 - \frac{5 \times 20}{100} $
-
Calculate the result:
$ D = 25 - \frac{100}{100} $
$ D = 25 - 1 $
$ D = 24\% $
Both methods show that the single discount equivalent to successive discounts of 5% and 20% is 24%.
Similar Questions
- An item marked for ₹38,800 is available on a discount of 25% or two successive discounts of 10% and 15%. What is the difference between the selling prices in the discount schemes?
- A wholesaler gives a scheme discount of 10% on a marked price of ₹400. What is the selling price?
- Find a single discount equivalent to successive discounts of 15% and 18%.
- A dealer offers successive discounts of 15% and 12% on a refrigerator marked at ₹25,000. What is the final selling price?
- How much percentage above the cost price should a shopkeeper mark his goods so that after allowing a discount 25% he should gain 12%?
- The marked price of a shirt is ₹500. If the shopkeeper offers a 20% discount, what is the selling price of the shirt?
- An article is marked for ₹720. If two successive discounts of 10% and 15% are allowed for sale, then the selling price of the article is:
- An electronics retailer offers two successive discounts of 7% and 10% on a TV priced at ₹48,000. What is the difference in the final price after applying two successive discounts compared to applying a flat discount of 17%?
- If on a marked price, the difference between selling prices with a discount of 45% and two successive discounts of 30% and 20% is ₹84, then the marked price is _______.
- A salesman offers 20% additional discount, after offering an initial discount of 25% on the labelled rate of a laptop. If the final sale price of the laptop is ₹18,000, then what was its labelled rate?
Important Questions from Discount and MP
The marked price of an article is Rs. 1500. A shopkeeper sells it by giving 20% discount on its marked price. If the cost price of the article is Rs. 991, then his profit (in Rs.) is:
Surbhi sold an article for Rs. 176 after giving 12% discount on its marked price. Had she not given any discount; she would have earned a profit of 25%. What is the cost price (in Rs.) of the article?
The marked price of an article is Rs. 240. A shopkeeper sells it by allowing 18% discount on its marked price and still gains 23%. What is the cost price (in Rs.) of the article?
Three shopkeepers A, B and C marked on an identical article at Rs. 4820. A, B and C sold their article on successive discounts of 20% and 20%; 25% and 15%; 30% and 10% respectively. Which shopkeeper gives the maximum discount and how much (in Rs.)?
Find a single discount percentage equivalent to successive discounts of 10%, 20% and 25%.
