Understanding the Successive Discounts Problem

This question involves calculating a second discount percentage when an article's marked price and final selling price are known, along with the first discount percentage.

Given Information:

• Marked Price (MP) of the article = ₹ 7,500
• Final Selling Price (SP) = ₹ 5,805
• First Discount (D₁) = 10%
• Second Discount (D₂) = ? (This is what we need to find)

Step-by-Step Calculation of the Second Discount

Step 1: Calculate the price after the first discount.

The first discount of 10% is applied to the marked price.

Amount of the first discount = $10\%$ of ₹ 7,500

Amount of D₁ = $\frac{10}{100} \times 7500 = \frac{1}{10} \times 7500 = ₹ 750$

Price after the first discount (let's call this Intermediate Price, IP) is:

IP = Marked Price - Amount of D₁

IP = $7500 - 750 = ₹ 6,750$

Step 2: Calculate the amount of the second discount.

The second discount is applied to the intermediate price (the price after the first discount). The final selling price is achieved after applying this second discount.

Amount of the second discount = Intermediate Price - Final Selling Price

Amount of D₂ = $6750 - 5805 = ₹ 945$

Step 3: Calculate the second discount percentage.

The second discount percentage is calculated based on the intermediate price.

Second Discount Percentage (D₂) = $\left( \frac{\text{Amount of D}_2}{\text{Intermediate Price}} \right) \times 100$

D₂ = $\left( \frac{945}{6750} \right) \times 100$

To simplify the fraction $\frac{945}{6750}$:

• Divide both by 5: $\frac{189}{1350}$
• Divide both by 9: $\frac{21}{150}$
• Divide both by 3: $\frac{7}{50}$

So, D₂ = $\frac{7}{50} \times 100 = 7 \times 2 = 14\%$

Conclusion

The second discount given on the article was 14%.

This matches option 4.