- Basic Math and Science Ratios, Proportions, and Percentages Questions and Answers Flashcards

A chemical solution is 40% acid by volume. After adding 50 mL of pure acid, the solution becomes 50% acid. What was the original volume of the solution?

Answer: 200 mL

Let the original volume be V. Original acid = 0.40V. After adding 50 mL acid: (0.40V + 50) / (V + 50) = 0.50. Solving: 0.40V + 50 = 0.50V + 25 → 25 = 0.10V → V = 250 mL is the new volume, but original was 250 - 50 = 200 mL.

Two gears are meshed together. Gear A has 45 teeth and Gear B has 30 teeth. If Gear A rotates at 120 RPM, what is the gear ratio of Gear A to Gear B, and at what speed does Gear B rotate?

Answer: 3:2 ratio; Gear B rotates at 180 RPM

Gear ratio A:B = 45:30 = 3:2. For meshed gears, speed is inversely proportional to the number of teeth: Speed_B = (Teeth_A / Teeth_B) × Speed_A = (45/30) × 120 = 1.5 × 120 = 180 RPM.

A substance loses 20% of its mass on the first heating and then loses 25% of its remaining mass on the second heating. What single percentage loss is equivalent to both heatings combined?

Answer: 40%

After first heating, 80% remains. After second heating, 75% of 80% remains = 0.75 × 0.80 = 0.60, or 60% of the original. Total loss = 40%. Note: you cannot simply add 20% + 25% = 45% because the second percentage applies to a reduced mass.

A map uses a scale where 3 cm represents 45 km. On the same map, two cities appear 7.5 cm apart. A scientist needs to travel between these cities but can only cover terrain at a rate of 60 km per hour. How long will the travel take?

Answer: 1 hour 52.5 minutes

Map scale: 3 cm = 45 km → 1 cm = 15 km. Actual distance = 7.5 × 15 = 112.5 km. Time = distance / speed = 112.5 / 60 = 1.875 hours = 1 hour and 52.5 minutes.

In a laboratory, a 12% saline solution and a 4% saline solution must be mixed to create 200 mL of an 8.5% saline solution. How much of the 12% solution is needed?

Answer: 112.5 mL

Let x = volume of 12% solution. Then (200 - x) = volume of 4% solution. Equation: 0.12x + 0.04(200 - x) = 0.085(200). Simplify: 0.12x + 8 - 0.04x = 17 → 0.08x = 9 → x = 112.5 mL.

A population of bacteria doubles every 3 hours. If the initial count is 500, what percentage increase occurs between hour 6 and hour 9?

Answer: 100%

At hour 6 (2 doublings): 500 × 2² = 2,000 bacteria. At hour 9 (3 doublings): 500 × 2³ = 4,000 bacteria. Percentage increase from hour 6 to 9 = (4,000 - 2,000) / 2,000 × 100 = 100%. Each doubling always represents a 100% increase over the previous count, regardless of absolute numbers.