Calculating Successive Discounts: Finding the Unknown Percentage

This problem involves calculating an unknown discount percentage when multiple successive discounts are applied to an article.

Understanding the Terms

• Marked Price (MP): This is the price tag on the article, ₹450 in this case.
• Selling Price (SP): This is the final price at which the article is sold after all discounts are applied, ₹267.30.
• Successive Discounts: These are multiple discounts applied one after another. If the discounts are d1%, d2%, and d3%, the final selling price is calculated sequentially.

Given Information

• Marked Price (MP) = ₹450
• Selling Price (SP) = ₹267.30
• First Discount = 10%
• Second Discount = x%
• Third Discount = 20%

Formula for Successive Discounts

The selling price (SP) after applying successive discounts can be calculated using the formula:

$$ SP = MP \times \left(1 - \frac{d1}{100}\right) \times \left(1 - \frac{d2}{100}\right) \times \left(1 - \frac{d3}{100}\right) $$

Where:

• MP is the Marked Price
• SP is the Selling Price
• d1, d2, d3 are the discount percentages

Step-by-Step Calculation

Let's substitute the given values into the formula:

$$ 267.30 = 450 \times \left(1 - \frac{10}{100}\right) \times \left(1 - \frac{x}{100}\right) \times \left(1 - \frac{20}{100}\right) $$

1. Calculate the value of the first discount factor: $$ \left(1 - \frac{10}{100}\right) = \left(1 - 0.10\right) = 0.90 $$
2. Calculate the value of the third discount factor: $$ \left(1 - \frac{20}{100}\right) = \left(1 - 0.20\right) = 0.80 $$
3. Substitute these values back into the equation: $$ 267.30 = 450 \times 0.90 \times \left(1 - \frac{x}{100}\right) \times 0.80 $$
4. Multiply the known factors: $$ 450 \times 0.90 \times 0.80 = 450 \times 0.72 = 324 $$
5. Now the equation simplifies to: $$ 267.30 = 324 \times \left(1 - \frac{x}{100}\right) $$
6. Isolate the term containing x: $$ \left(1 - \frac{x}{100}\right) = \frac{267.30}{324} $$
7. Perform the division: $$ \frac{267.30}{324} = 0.825 $$
8. So, the equation becomes: $$ 1 - \frac{x}{100} = 0.825 $$
9. Solve for $\frac{x}{100}$: $$ \frac{x}{100} = 1 - 0.825 $$ $$ \frac{x}{100} = 0.175 $$
10. Solve for x: $$ x = 0.175 \times 100 $$ $$ x = 17.5 $$

Conclusion

The value of the unknown successive discount, x, is 17.5%. This means the three successive discounts were 10%, 17.5%, and 20%.