NBT NBT Quantitative Literacy: Ratios, Proportions and Rates 3 — Questions and Answers
Question 1: A school's learner-to-teacher ratio is 35:1. If there are 7 teachers, how many learners are there?
- 245 (Correct answer)
- 280
- 210
- 350
Correct answer: 245
Learners = 35 × 7 = 245.
Question 2: A runner completes a 10 km race in 50 minutes. What is her average speed in km/h?
- 12 km/h (Correct answer)
- 10 km/h
- 15 km/h
- 8 km/h
Correct answer: 12 km/h
Speed = 10 ÷ (50/60) = 10 × (60/50) = 12 km/h.
Question 3: A model car is built at a scale of 1:24. The real car is 4.2 m long. How long is the model car in cm?
- 17.5 cm (Correct answer)
- 10.08 cm
- 100.8 cm
- 42 cm
Correct answer: 17.5 cm
4.2 m = 420 cm; model length = 420 ÷ 24 = 17.5 cm.
Question 4: A grocery store sells 1.5 litres of juice for R18 and 2 litres for R22. Which is the better value?
- 2-litre bottle (Correct answer)
- 1.5-litre bottle
- Both are equal value
- Cannot be determined
Correct answer: 2-litre bottle
1.5 L: R18/1.5 = R12/L; 2 L: R22/2 = R11/L — the 2-litre bottle is cheaper per litre.
Question 5: If y is inversely proportional to x and y = 8 when x = 3, what is y when x = 12?
- 2 (Correct answer)
- 32
- 4
- 6
Correct answer: 2
Constant k = 8 × 3 = 24; y = 24 ÷ 12 = 2.
Question 6: A fertiliser bag states 'apply at 30 g per m²'. How many kilograms are needed for a 500 m² garden?
- 15 kg (Correct answer)
- 150 kg
- 1.5 kg
- 3 kg
Correct answer: 15 kg
Total = 30 × 500 = 15 000 g = 15 kg.
Question 7: Three friends invest R5 000, R3 000, and R2 000 in a business. At the end of the year the profit is R12 000. How much does the friend who invested R3 000 receive?
- R3 600 (Correct answer)
- R4 000
- R3 000
- R2 400
Correct answer: R3 600
Ratio = 5:3:2; total parts = 10; middle friend's share = (3/10) × 12 000 = R3 600.
NBT NBT Quantitative Literacy: Ratios, Proportions and Rates 3
A school's learner-to-teacher ratio is 35:1.
If there are 7 teachers, how many learners are there?