Which of the following statements are true? (A) A single discount equivalent…
2024
Which of the following statements are true?
(A) A single discount equivalent to successive discounts of 20%, 10% and 5% is 35%.
(B) If an article is sold for ₹209 after successive discounts of 12% and 5%, its original price is ₹250.
(C) If a shopkeeper gives two successive discounts of 5% each on a marked price of ₹80, the selling price is ₹75.
(D) If the difference between a single discount of 35% and two successive discounts of 20% each on a bill is ₹22, the total bill amount is ₹2200.
Choose the correct answer from the options given below.
Answer: C. (B) and (D) Only — ConceptFor successive percentage discounts, multiply the retained-price factors rather than adding the discount rates. After discounts d1, d2, …, the selling…
- A.
(A), (B) and (C) Only
- B.
(A) and (C) Only
- C.
(B) and (D) Only
- D.
(C) and (D) Only
Attempted by 1 students.
Show answer & explanation
Correct answer: C
Concept
For successive percentage discounts, multiply the retained-price factors rather than adding the discount rates.
After discounts d1, d2, …, the selling price is MP × (1 − d1/100) × (1 − d2/100) × …; the equivalent discount is 100% minus the retained percentage. A difference between discount amounts equals the difference between their effective rates multiplied by the base amount.
Application
Statement (A): The retained fraction is 0.80 × 0.90 × 0.95 = 0.684, so the equivalent discount is (1 − 0.684) × 100% = 31.6%, not 35%. Thus (A) is false.
Statement (B): Let the original price be P. Then P × 0.88 × 0.95 = 209, so P = 209/0.836 = 250. Thus (B) is true.
Statement (C): The selling price is ₹80 × 0.95 × 0.95 = ₹72.20, not ₹75. Thus (C) is false.
Statement (D): Two successive discounts of 20% give an effective discount of 1 − (0.80 × 0.80) = 36%. Its difference from 35% is 1%. If 1% equals ₹22, the bill amount is ₹22/0.01 = ₹2200. Thus (D) is true.
Cross-check
For (B), ₹250 × 0.88 × 0.95 = ₹209, which reproduces the stated selling price.
For (D), 36% of ₹2200 is ₹792 and 35% is ₹770; the difference is ₹22.
Result
Statements (B) and (D) are true, so the correct combination is “(B) and (D) Only”.