Calculating Selling Price with Successive Discounts

Understanding how successive discounts work is important for calculating the final price of an item. A successive discount means a discount is applied, and then another discount is applied to the reduced price, and so on.

In this problem, we are given:

• Marked Price (MP) = Rs 3000
• Three successive discounts of 10% each.

We need to find the Selling Price (SP) after applying these three discounts.

Step-by-Step Selling Price Calculation

We can calculate the price after each discount individually.

After the First 10% Discount:

The first discount is 10% on the Marked Price of Rs 3000.

Discount amount = 10% of Rs 3000

Discount amount $= \frac{10}{100} \times 3000 = 0.10 \times 3000 = 300$

Price after first discount = Marked Price - Discount amount

Price after first discount $= 3000 - 300 = 2700$

Alternatively, if a 10% discount is given, the customer pays 100% - 10% = 90% of the price.

Price after first discount $= 90\% \text{ of } 3000 = \frac{90}{100} \times 3000 = 0.90 \times 3000 = 2700$

Price after the first discount is Rs 2700.

After the Second 10% Discount:

The second discount of 10% is applied to the price after the first discount, which is Rs 2700.

Discount amount = 10% of Rs 2700

Discount amount $= \frac{10}{100} \times 2700 = 0.10 \times 2700 = 270$

Price after second discount = Price after first discount - Discount amount

Price after second discount $= 2700 - 270 = 2430$

Alternatively, price after second discount $= 90\% \text{ of } 2700 = \frac{90}{100} \times 2700 = 0.90 \times 2700 = 2430$

Price after the second discount is Rs 2430.

After the Third 10% Discount:

The third discount of 10% is applied to the price after the second discount, which is Rs 2430.

Discount amount = 10% of Rs 2430

Discount amount $= \frac{10}{100} \times 2430 = 0.10 \times 2430 = 243$

Selling Price = Price after second discount - Discount amount

Selling Price $= 2430 - 243 = 2187$

Alternatively, Selling Price $= 90\% \text{ of } 2430 = \frac{90}{100} \times 2430 = 0.90 \times 2430 = 2187$

The selling price after three successive discounts of 10% is Rs 2187.

Calculation Using Formula for Successive Discounts

The final Selling Price (SP) after successive discounts $d_1\%$, $d_2\%$, $d_3\%$ on a Marked Price (MP) can be calculated using the formula:

$SP = MP \times \left(1 - \frac{d_1}{100}\right) \times \left(1 - \frac{d_2}{100}\right) \times \left(1 - \frac{d_3}{100}\right)$

In this case, $MP = 3000$, $d_1 = 10$, $d_2 = 10$, $d_3 = 10$.

$SP = 3000 \times \left(1 - \frac{10}{100}\right) \times \left(1 - \frac{10}{100}\right) \times \left(1 - \frac{10}{100}\right)$

$SP = 3000 \times \left(1 - 0.10\right) \times \left(1 - 0.10\right) \times \left(1 - 0.10\right)$

$SP = 3000 \times (0.90) \times (0.90) \times (0.90)$

$SP = 3000 \times (0.90)^3$

$SP = 3000 \times 0.729$

$SP = 2187$

The Selling Price is Rs 2187.

Summary of Calculation Steps

The calculated selling price is Rs 2187.

Revision Table: Key Concepts in Discounts

Additional Information on Equivalent Single Discount

Sometimes, it's useful to know what single discount would be equivalent to a series of successive discounts. For two successive discounts of $d_1\%$ and $d_2\%$, the equivalent single discount (D%) is given by:

$D = d_1 + d_2 - \frac{d_1 \times d_2}{100}$

For three successive discounts $d_1\%$, $d_2\%$, and $d_3\%$, you can first find the equivalent single discount for $d_1$ and $d_2$, let's call it $D_{12}$. Then, find the equivalent single discount for $D_{12}$ and $d_3$.

In our case, with three 10% discounts ($d_1=10, d_2=10, d_3=10$):

Equivalent single discount for the first two 10% discounts:

$D_{12} = 10 + 10 - \frac{10 \times 10}{100} = 20 - \frac{100}{100} = 20 - 1 = 19\%$

Now, equivalent single discount for $D_{12}$ (19%) and the third 10% discount:

$D = 19 + 10 - \frac{19 \times 10}{100} = 29 - \frac{190}{100} = 29 - 1.9 = 27.1\%$

So, three successive discounts of 10% are equivalent to a single discount of 27.1%.

We can verify this: Selling Price = MP - (Equivalent Single Discount % of MP)

Selling Price $= 3000 - \left(\frac{27.1}{100} \times 3000\right)$

Selling Price $= 3000 - (0.271 \times 3000)$

Selling Price $= 3000 - 813 = 2187$

This confirms that the selling price is indeed Rs 2187.