A tyre is sold at three successive discounts of 20%, 30% and 20% on its marked price. What is the net single equivalent discount (in percentage) on the marked price?

Introduction / Context:
This problem deals with successive discounts. When a shopkeeper offers several discounts one after another on the same marked price, the overall reduction cannot be found by simply adding the individual percentages. Instead, each discount acts on the already reduced price. The question asks for the net single discount that would give the same final selling price as the three successive discounts of 20%, 30% and 20%.

Given Data / Assumptions:
- Marked price (MP) of a tyre is some amount, say M rupees.
- First discount = 20 percent.
- Second discount = 30 percent on the reduced price after the first discount.
- Third discount = 20 percent on the price after the second discount.
- We must find the equivalent single discount percentage on M that gives the same final price.

Concept / Approach:
Each discount is implemented by multiplying the current price by a factor (1 - discount / 100). The final price factor after all discounts is the product of the individual factors. Once we know the final factor relative to the marked price, the net discount is 1 minus this factor, converted into a percentage. This method is analogous to successive percentage change problems in general.

Step-by-Step Solution:
Let the marked price be M. First discount 20% means factor = 1 - 20 / 100 = 0.80. Second discount 30% means factor = 1 - 30 / 100 = 0.70. Third discount 20% again means factor = 1 - 20 / 100 = 0.80. Final selling price factor = 0.80 * 0.70 * 0.80. Compute 0.80 * 0.70 = 0.56. Then 0.56 * 0.80 = 0.448. So final selling price = 0.448M. Net discount fraction = 1 - 0.448 = 0.552. Net discount percentage = 0.552 * 100 = 55.2 percent.

Verification / Alternative check:
Assume a marked price of Rs. 1000 for an easy numerical example. After the first 20% discount, price becomes 1000 * 0.80 = 800. After the second 30% discount, the price becomes 800 * 0.70 = 560. After the third 20% discount, the price becomes 560 * 0.80 = 448. The total discount is 1000 - 448 = 552, which is 55.2% of 1000. This confirms the net discount we calculated.

Why Other Options Are Wrong:
59.6, 62.8 and 51.4: These values result from incorrect multiplication of factors or from naive addition of percentages without considering the reduced bases. They do not match the correct final price factor 0.448.
48.0: This is much too small and could come from averaging the three discounts rather than computing their combined effect.

Common Pitfalls:
Students often add discounts directly (20 + 30 + 20 = 70) or average them, both of which are wrong. Every discount applies to a new base, which is the reduced price after the previous discount. Forgetting this leads to large errors. The correct method is always to convert each discount to its multiplicative factor and multiply them to get the final factor.

Final Answer:
The net single equivalent discount on the tyre is 55.2 percent of the marked price.