Multiple choice

Passage

Directions: Study the given information and answer the following question. The following table gives the discount offered by 5 different hardware stores on various items. Shop/Item Nuts Bolts Washers Screws Shop A - - 10% 10% Shop B - - 5% - Shop C 10% - - - Shop D - 5% - 10% Shop E - - - -

If shop A offers two successive discounts of the same percentage as shop D does once on bolts, and if they both sell at the same price, then what will be the ratio of the marked price at shop D to that at shop A?

  1. 90 : 95

  2. 95 : 90

  3. 95 : 100

  4. 100 : 95

  5. None of these
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Shop D offers 5% discount on bolts. Shop A offers two successive discounts of 5% each. Let marked price at D be Md and at A be Ma. Selling price D = Md * 0.95. Selling price A = Ma * 0.95 * 0.95. Equating them: Md * 0.95 = Ma * 0.95 * 0.95, so Md / Ma = 0.95 / 1 = 95 / 100.

AI explanation

Shop D offers a 5% discount on bolts, so shop A offers two successive 5% discounts. Let the marked price at shop A be MP_A and at shop D be MP_D. Their selling prices are equal, so MP_A * 0.95 * 0.95 = MP_D * 0.95. This simplifies to MP_A * 0.95 = MP_D. The ratio of the marked price at shop D to that at shop A is MP_D / MP_A = 0.95. Thus, the required ratio is 95 : 100.

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