BSEP - Basic Skills Education Program Ratios and Proportions Questions and Answers — Questions and Answers
Question 1: A military map has a scale of 1:50,000. If the distance between two points on the map is 4.5 centimeters, what is the actual ground distance between the two points in kilometers?
- 22.5 km
- 0.225 km
- 225 km
- 2.25 km (Correct answer)
Correct answer: 2.25 km
The scale 1:50,000 means 1 unit on the map equals 50,000 of the same units on the ground. Therefore, 4.5 cm on the map represents 4.5 * 50,000 = 225,000 cm on the ground. To convert centimeters to kilometers, you divide by 100,000 (since there are 100 cm in a meter and 1,000 meters in a kilometer). So, 225,000 cm / 100,000 = 2.25 km.
Question 2: A piece of equipment requires a fuel-oil mixture with a ratio of 40:1 (40 parts gasoline to 1 part oil). If a container is filled with 5 gallons of gasoline, how many fluid ounces of oil must be added? (Note: 1 gallon = 128 fluid ounces)
- 12.8 oz
- 16 oz (Correct answer)
- 3.2 oz
- 8 oz
Correct answer: 16 oz
First, convert the 5 gallons of gasoline to fluid ounces: 5 gallons * 128 fl oz/gallon = 640 fl oz. The ratio is 40 parts gasoline to 1 part oil. Set up the proportion: 40/1 = 640/x. Cross-multiply to solve for x: 40x = 640. Divide both sides by 40: x = 16 fluid ounces.
Question 3: In a simple gear system, a drive gear with 60 teeth is meshed with a driven gear with 20 teeth. Which of the following correctly expresses the gear ratio of the drive gear to the driven gear?
- 1:3
- 3:1 (Correct answer)
- 6:2
- 20:60
Correct answer: 3:1
The gear ratio is the ratio of the number of teeth on the drive gear to the number of teeth on the driven gear. This is expressed as 60:20. To simplify, divide both numbers by their greatest common divisor, which is 20. 60 ÷ 20 = 3 and 20 ÷ 20 = 1. The simplified ratio is 3:1.
Question 4: A vertical flagpole casts a shadow 12 feet long. At the same time, a soldier who is 6 feet tall casts a shadow 4 feet long. What is the height of the flagpole?
- 14 feet
- 20 feet
- 18 feet (Correct answer)
- 24 feet
Correct answer: 18 feet
This is a problem of similar triangles. The ratio of an object's height to its shadow's length is the same for both the soldier and the flagpole. Set up the proportion: (soldier's height) / (soldier's shadow) = (flagpole's height) / (flagpole's shadow). This gives 6/4 = H/12. Cross-multiply to get 4 * H = 6 * 12, or 4H = 72. Divide by 4 to find H = 18 feet.
Question 5: A maintenance check finds that 5% of the vehicles in a motor pool are not mission-capable. Which of the following represents the ratio of mission-capable vehicles to non-mission-capable vehicles?
- 1:20
- 20:1
- 1:19
- 19:1 (Correct answer)
Correct answer: 19:1
If 5% of vehicles are non-mission-capable, then 100% - 5% = 95% are mission-capable. The ratio of mission-capable to non-mission-capable is 95 to 5, or 95:5. To simplify this ratio, divide both numbers by their greatest common divisor, which is 5. 95 ÷ 5 = 19, and 5 ÷ 5 = 1. The simplified ratio is 19:1.
Question 6: If 3 soldiers can dig a trench 10 meters long in 2 hours, how long would it take 5 soldiers, working at the same rate, to dig a trench 25 meters long?
- 3 hours (Correct answer)
- 2.5 hours
- 4 hours
- 3.5 hours
Correct answer: 3 hours
First, calculate the total work in 'soldier-hours' for the first task: 3 soldiers * 2 hours = 6 soldier-hours to dig 10 meters. This establishes a work rate of 10 meters per 6 soldier-hours. For the new task of digging 25 meters, set up a proportion: (10 meters / 6 soldier-hours) = (25 meters / x soldier-hours). Solving for x gives x = (25 * 6) / 10 = 15 soldier-hours. With 5 soldiers, the time required is 15 soldier-hours / 5 soldiers = 3 hours.
