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NBT Quantitative Literacy: Ratios, Proportions and Rates Flashcards

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

Read the first 6 NBT Quantitative Literacy: Ratios, Proportions and Rates flashcards as text

  1. A car travels from City A to City B at 90 km/h and returns along the same route at 60 km/h. What is the average speed for the entire round trip?

    Answer: 72 km/h

    Average speed for equal distances uses the harmonic mean: 2 × (90 × 60) ÷ (90 + 60) = 10 800 ÷ 150 = 72 km/h. The arithmetic mean (75 km/h) is wrong because the car spends more time travelling at the slower speed, pulling the true average below 75.

  2. A recipe requires flour, sugar, and butter in the ratio 5 : 2 : 1. You want to increase only the flour by 20% while keeping sugar and butter amounts unchanged. What is the new ratio of flour : sugar : butter?

    Answer: 6 : 2 : 1

    Original parts — flour: 5, sugar: 2, butter: 1. Increasing only flour by 20% gives 5 × 1.2 = 6. Sugar and butter stay at 2 and 1 respectively. New ratio = 6 : 2 : 1. The other options incorrectly scale sugar or butter as well.

  3. Pipe A fills a tank in 6 hours; Pipe B drains it in 9 hours. Both pipes are opened when the tank is exactly one-third full. How long will it take to fill the tank completely?

    Answer: 12 hours

    Net fill rate = 1/6 − 1/9 = 3/18 − 2/18 = 1/18 of the tank per hour. Remaining fraction to fill = 1 − 1/3 = 2/3. Time = (2/3) ÷ (1/18) = (2/3) × 18 = 12 hours.

  4. A map uses a scale of 1 : 250 000. Two towns measure 7.4 cm apart on the map. The actual road between them is not straight — it is 15% longer than the straight-line distance. What is the length of the road in kilometres?

    Answer: 21.275 km

    Straight-line real distance = 7.4 cm × 250 000 = 1 850 000 cm = 18.5 km. The road is 15% longer: 18.5 × 1.15 = 21.275 km. Choosing 18.5 km ignores the detour; 23.1 km over-applies the percentage.

  5. Two workers can complete a project together in 8 days. Worker A alone takes 12 days. Worker B works alone for 4 days, then A joins him. How many additional days do they work together to finish the project?

    Answer: 6⅔ days

    A's rate = 1/12 per day. Combined rate = 1/8 per day, so B's rate = 1/8 − 1/12 = 1/24 per day. B alone for 4 days completes 4/24 = 1/6. Remaining = 5/6. Together at rate 1/8: time = (5/6) ÷ (1/8) = 40/6 = 6⅔ days.

  6. A 140 mL solution is 35% acid by volume. Pure water is added until the solution becomes exactly 20% acid. How much water is added?

    Answer: 105 mL

    Pure acid present = 35% × 140 = 49 mL. This acid must equal 20% of the final volume V: 0.20 × V = 49, so V = 245 mL. Water added = 245 − 140 = 105 mL. The other options result from incorrect proportional reasoning that does not keep the acid volume fixed.