Compare successive discount schemes: A retailer offers four discount schemes on the same article: (i) 10% followed by 10% (ii) 12% followed by 8% (iii) 15% followed by 5% (iv) Flat 20% Under which scheme is the selling price minimum?

Difficulty: Easy

i
ii
iii
iv
All equal

Correct Answer: iv

Explanation:

Introduction / Context:
Successive discounts multiply, not add. To find the minimum selling price (SP), compute the net retention factor (fraction of MP paid) under each scheme and compare.

Given Data / Assumptions:
Let MP = 1 (or 100%). Compute the factor after each scheme.

Concept / Approach:
For successive discounts d1 and d2, net factor = (1 − d1)*(1 − d2). For a single discount d, factor = 1 − d. The smallest factor gives the minimum SP.

Step-by-Step Solution:

(i) 0.90 * 0.90 = 0.81 ⇒ 19% net (ii) 0.88 * 0.92 = 0.8096 ⇒ 19.04% net (iii) 0.85 * 0.95 = 0.8075 ⇒ 19.25% net (iv) 1 − 0.20 = 0.80 ⇒ 20% net Minimum SP corresponds to the smallest factor, which is 0.80 (scheme iv).

Verification / Alternative check:
Try MP = ₹100; resulting SPs are ₹81, ₹80.96, ₹80.75, and ₹80; the minimum is ₹80 under scheme (iv).

Why Other Options Are Wrong:
i, ii, iii produce higher SPs than iv based on the computed factors.

Common Pitfalls:
Adding discounts (e.g., 10% + 10% = 20%) without compounding leads to wrong comparisons.

Compare successive discount schemes: A retailer offers four discount schemes on the same article: (i) 10% followed by 10% (ii) 12% followed by 8% (iii) 15% followed by 5% (iv) Flat 20% Under which scheme is the selling price minimum?

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