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Ratios, Proportions, and Percentages Flashcards

6 cards from real BMST practice questions. Tap to flip, then mark Knew It or Still Learning — missed cards come back until you master them.

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  1. A chemical solution is prepared by mixing acid and water in a 3:7 ratio. An existing batch contains 30 L of acid and 70 L of water. If 15 additional liters of acid are poured in, what is the new acid-to-water ratio in simplest form?

    Answer: 9:14

    After adding 15 L of acid: 30+15 = 45 L acid, 70 L water unchanged. Ratio = 45:70. Divide both by 5 → 9:14.

  2. A retailer marks up an item by 40% above wholesale cost, then applies a 25% discount on the marked-up price. What is the net percentage change relative to the original wholesale price?

    Answer: 5% increase

    Start at 100. After 40% markup: 100 × 1.40 = 140. After 25% discount: 140 × 0.75 = 105. Net change = +5%. The two changes do not cancel — the discount applies to the higher price, leaving a net gain of 5%.

  3. Two quantities X and Y are in the ratio 5:8. X is increased by 60% and Y is decreased by 25%. What is the new ratio of X to Y?

    Answer: 4:3

    Let X = 5k and Y = 8k. New X = 5k × 1.60 = 8k. New Y = 8k × 0.75 = 6k. New ratio = 8k:6k = 4:3.

  4. A pipe fills a tank in 6 hours; a drain empties it in 9 hours. The tank is already 1/3 full when both are opened simultaneously. How many hours until the tank is completely full?

    Answer: 12

    Net fill rate = 1/6 − 1/9 = 3/18 − 2/18 = 1/18 per hour. Remaining capacity = 2/3. Time = (2/3) ÷ (1/18) = 12 hours.

  5. In a class the ratio of boys to girls is 4:5. After 8 boys and 5 girls join, the ratio becomes 6:7. How many students were in the class originally?

    Answer: 117

    Let boys = 4k, girls = 5k. After joining: (4k+8)/(5k+5) = 6/7. Cross-multiply: 28k+56 = 30k+30 → 2k = 26 → k = 13. Original total = 9 × 13 = 117.

  6. A solution is 20% salt by mass. Water evaporates (no salt is lost) until the concentration rises to 25%. What percentage of the original water was removed?

    Answer: 25%

    Use 100 g as a base: 20 g salt + 80 g water. After evaporation, salt (20 g) must equal 25% of the new total: 20/0.25 = 80 g total. New water = 80−20 = 60 g. Water removed = 80−60 = 20 g. As a percentage of original water: 20/80 = 25%.