Finding Selling Price with Successive Discounts
This problem involves calculating the final selling price of an article after applying two consecutive percentage discounts to its marked price.
Understanding the Terms
- Marked Price (MP): This is the price tag on the article, ₹800 in this case.
- Successive Discounts: These are discounts applied one after another. The second discount is calculated on the price obtained after the first discount, not on the original marked price.
- Selling Price (SP): This is the final price at which the article is sold to the customer after all discounts are applied.
Step-by-Step Calculation
The marked price (MP) is given as ₹800.
There are two successive discounts:
- First discount = 24%
- Second discount = 15%
Calculating the Price After the First Discount
The first discount is 24% of the marked price.
Discount Amount 1 = $24\%$ of ₹800
Discount Amount 1 = $ \frac{24}{100} \times 800 $
Discount Amount 1 = $ 24 \times 8 $
Discount Amount 1 = $ ₹192 $
Price after the first discount = Marked Price - Discount Amount 1
Price after first discount = $ ₹800 - ₹192 $
Price after first discount = $ ₹608 $
Calculating the Price After the Second Discount
The second discount is 15% of the price after the first discount (which is ₹608).
Discount Amount 2 = $15\%$ of ₹608
Discount Amount 2 = $ \frac{15}{100} \times 608 $
Discount Amount 2 = $ 0.15 \times 608 $
Discount Amount 2 = $ ₹91.20 $
The final selling price (SP) is the price after the first discount minus the second discount amount.
Selling Price = Price after first discount - Discount Amount 2
Selling Price = $ ₹608 - ₹91.20 $
Selling Price = $ ₹516.80 $
Alternative Calculation Method
We can also calculate the selling price directly using the formula:
SP = MP $ \times (1 - \frac{\text{Discount 1}}{100}) \times (1 - \frac{\text{Discount 2}}{100}) $
SP = $ 800 \times (1 - \frac{24}{100}) \times (1 - \frac{15}{100}) $
SP = $ 800 \times (1 - 0.24) \times (1 - 0.15) $
SP = $ 800 \times (0.76) \times (0.85) $
SP = $ 800 \times 0.646 $
SP = $ 516.80 $
Conclusion
Therefore, the selling price of the article after applying the two successive discounts of 24% and 15% is ₹516.80.
Important Questions from Profit and Loss
- Veer bought some sharpeners at the rate of ₹180/dozen. He sold them for ₹23 each. His profit percentage is ____ % (rounded off to two decimal places).
- A shopkeeper lists the price of a fan at 60% above its cost price and offers a 15% discount on its list price. If he earns a profit of ₹117, then what is the list price (in ₹) of the fan?
- A discount of 13% on the marked price of an article is allowed and then the article is sold for ₹348. The marked price of the article is:
- A trader claims to sell grains at a profit of 29%, but also dishonestly uses a weight which is 13% less than what is mentioned on it. Find the total percentage of profit earned by the trader. (Round off the answer to the nearest whole number.)
- 56 tube lights were purchased for ₹56, and 20 tube lights broke in transit. The trader sold the remaining tube lights at ₹4.60 each. Find his profit.
