A shopkeeper gives two successive discounts of 20% and 30% on the marked price of an article. What is the single equivalent discount percentage on the article?

Introduction / Context:

This question checks your understanding of successive discounts, a standard topic under percentage and profit and loss. Many shoppers and exam candidates mistakenly add discounts directly, but in reality each discount is applied on the reduced price, not on the original price. You are asked to find the net or equivalent single discount.

Given Data / Assumptions:

• First discount = 20% on the marked price.
• Second discount = 30% on the already reduced price.
• There is one marked price for the article.
• We need the single discount that gives the same final selling price.

Concept / Approach:

When two successive discounts are given, we multiply the remaining price factors. A 20% discount leaves 80% of the price, which is a factor 0.80. A 30% discount leaves 70% of the price, or factor 0.70. The combined factor is 0.80 * 0.70. The net discount is 1 minus this combined factor, converted to a percentage.

Step-by-Step Solution:

Verification / Alternative check:

Assume a simple marked price, say M = Rs 100. After a 20% discount, price becomes Rs 80. After a further 30% discount, price becomes 70% of 80, which is 0.70 * 80 = Rs 56. The overall discount from Rs 100 is Rs 44, that is 44%. This numeric check supports the earlier factor method.

Why Other Options Are Wrong:

• 40%: This is simply 20% + 20% (a miscalculation) or sometimes guessed incorrectly. It ignores the compounding effect.
• 56%: This would imply the customer pays only 44% of the price, but we computed that they pay 56% of the price, not the other way round.
• 50%: This is just an average and has no mathematical basis in the given situation.
• 60%: This is clearly too high compared to giving 20% and 30% sequentially.

Common Pitfalls:

A very common error is to directly add the discounts (20% + 30% = 50%) and claim 50% as the net discount. However, the second discount is taken on the already reduced price, so the base changes. Another mistake is to confuse the fraction of price remaining with the discount itself. Always convert each discount into a remaining percentage factor and multiply them to get the final paid percentage.

Final Answer:

The net equivalent discount is 44%.