A shopkeeper offers a ‘Buy 4, get 1 free’ scheme on an item marked at ₹800 per…
2026
A shopkeeper offers a ‘Buy 4, get 1 free’ scheme on an item marked at ₹800 per unit. After the scheme is applied, an additional cash discount of 10% is given on the payable amount. Find the effective discount percentage on the total marked price of the five items.
Answer: C. 28% — ConceptFor successive discounts of a% and b%, the equivalent discount is a + b − ab/100. Equivalently, multiply the fractions of the marked price that remain…
- A.
30%
- B.
29%
- C.
28%
- D.
27%
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Show answer & explanation
Correct answer: C
Concept
For successive discounts of a% and b%, the equivalent discount is a + b − ab/100. Equivalently, multiply the fractions of the marked price that remain after each discount.
A ‘buy m, get n free’ scheme gives m + n items for the marked price of m items, so its discount fraction is n/(m+n).
Application
Under ‘Buy 4, get 1 free’, five items are received while the marked price of four items is payable. The scheme discount is (1/5) × 100 = 20%.
After the scheme, 80% of the total marked price remains payable. The extra 10% cash discount leaves 90% of that amount: 0.80 × 0.90 = 0.72.
Thus the final payable amount is 72% of the total marked price, so the effective discount is 100% − 72% = 28%.
Cross-check
For five items, the total marked price is 5 × ₹800 = ₹4,000. Paying for four items gives ₹3,200; after 10% cash discount, the payment is ₹2,880. The discount is ₹4,000 − ₹2,880 = ₹1,120, and ₹1,120/₹4,000 × 100 = 28%.
Therefore, the effective discount on the total marked price is 28%.