A discount series of 15%, 20% and 25% is allowed successively on the marked price of an article. What single equivalent rate of discount is equal to this series of three discounts?

Introduction / Context:
This problem extends the idea of successive discounts to three levels: 15%, 20% and 25%. The objective is to find a single discount rate that would produce the same final selling price as applying these three discounts one after the other. Knowing how to combine several percentage reductions into one effective percentage is useful in understanding real life sale offers and is frequently tested in quantitative aptitude exams.

Given Data / Assumptions:

• Let the marked price of the article be M rupees.
• First discount = 15% on M.
• Second discount = 20% on the price after the first discount.
• Third discount = 25% on the price after the second discount.
• We need a single equivalent discount D% such that applying D% once to M gives the same final selling price.

Concept / Approach:
If a discount of d% is applied, then the remaining price factor is (1 − d/100). For multiple discounts, the total remaining factor is the product of the individual remaining factors. Here, the remaining factors will be 0.85 for 15%, 0.8 for 20% and 0.75 for 25%. Multiply these to get the final fraction of marked price that the buyer pays. The equivalent single discount is then 1 minus this fraction, converted to a percentage.

Step-by-Step Solution:
Step 1: Assume marked price = M. Step 2: After 15% discount, remaining fraction = 1 − 15/100 = 0.85. New price = 0.85M. Step 3: After 20% discount on this price, remaining fraction = 1 − 20/100 = 0.8. New price = 0.85M * 0.8 = 0.68M. Step 4: After 25% discount on this price, remaining fraction = 1 − 25/100 = 0.75. Final price = 0.68M * 0.75. Step 5: Multiply: 0.68 * 0.75 = 0.51. So final price = 0.51M. Step 6: This means the customer pays 51% of the marked price, so the single equivalent discount = 100% − 51% = 49%.

Verification / Alternative check:
We can test with an actual value, for example M = Rs 100. After 15% discount, price = 85. After 20% discount, price = 85 * 0.8 = 68. After 25% discount, price = 68 * 0.75 = 51. Thus the buyer finally pays Rs 51 on a Rs 100 marked price. This clearly shows a total effective discount of 100 − 51 = 49%, which matches the computed value. The numerical test confirms that our algebraic reasoning is correct.

Why Other Options Are Wrong:

• 48% or 50% are close but not equal to the exact discount of 49%; using them would give final prices slightly different from 51% of M.
• 51% discount would leave only 49% of M as the final price, which reverses the correct result.

Common Pitfalls:
Many students try to add the discount rates directly as 15% + 20% + 25% = 60%, which gives a greatly exaggerated effective discount. Others apply each discount to the original marked price instead of to the successively reduced prices. Some also commit calculation mistakes when multiplying decimals. To avoid errors, always convert each discount to a remaining factor, multiply them carefully, and only then subtract from 1 to get the equivalent single discount.

Final Answer:
The single equivalent rate of discount is 49%.