Successive discount versus a single discount: a motorcycle is displayed at Rs 50,000. Instead of a single 15% discount, the buyer is offered two successive discounts of 10% and 5%. Determine the single equivalent discount the buyer actually receives.

Introduction:Successive discounts do not add arithmetically; they combine multiplicatively. Converting a pair of discounts to a single equivalent discount is a standard skill in profit and loss and pricing questions.

Given Data / Assumptions:

• Marked price reference: any convenient base (e.g., Rs 100) works.
• Two successive discounts: first 10%, then 5% on the reduced price.
• We must find the single equivalent discount.

Concept / Approach:Let M be the marked price. After 10% off, price becomes 0.90M. After a further 5% off, price becomes 0.95 * 0.90M = 0.855M. The equivalent discount D satisfies price = (1 - D)M, i.e., 1 - D = 0.855.

Step-by-Step Solution:Net price factor = 0.90 * 0.95 = 0.855Equivalent discount D = 1 - 0.855 = 0.145Therefore, D = 14.5%

Verification / Alternative check:Using M = Rs 50,000 for concreteness: after 10% off, Rs 45,000; after 5% more, Rs 42,750. Single discount from Rs 50,000 to Rs 42,750 is Rs 7,250, which is 7,250 / 50,000 * 100 = 14.5%.

Why Other Options Are Wrong:

• 15%: simple addition ignores multiplicative compounding.
• 15.5%: an overcorrection; incorrect rounding.
• None of these: incorrect because 14.5% is exact.

Common Pitfalls:

• Adding percentages directly for successive discounts.
• Applying the second discount to the original price instead of the reduced price.

Final Answer:14.5%