Math Aptitude Basics: questions and answers
Study every question with its correct answer and explanation.
1. What is 20% of 450?
- A. 80
- B. 90
- C. 95
- D. 100
Answer: 90
20% of 450 = 450 × 20/100 = 90. Shortcut: 10% of 450 is 45, so 20% is 45 × 2 = 90.
2. The price of an item rises from 400 to 500. What is the percentage increase?
- A. 15%
- B. 20%
- C. 25%
- D. 30%
Answer: 25%
Increase = 500 − 400 = 100, and percentage increase = (100/400) × 100 = 25%. Note that if the price fell from 500 to 400, the decrease would be (100/500) × 100 = 20%, because the base value changes.
3. What is the simple interest on 5,000 at 8% per annum for 3 years?
- A. 1,200
- B. 1,000
- C. 1,500
- D. 1,320
Answer: 1,200
Simple interest = (P × R × T)/100 = (5000 × 8 × 3)/100 = 1,200. The total amount after 3 years would be 5,000 + 1,200 = 6,200.
4. 720 is divided in the ratio 5 : 3. What is the larger part?
- A. 270
- B. 360
- C. 400
- D. 450
Answer: 450
Total parts = 5 + 3 = 8, so one part = 720 ÷ 8 = 90. The larger part = 5 × 90 = 450 and the smaller part = 3 × 90 = 270 (check: 450 + 270 = 720).
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5. A speed of 72 km/h is equal to how many metres per second?
- A. 15 m/s
- B. 18 m/s
- C. 20 m/s
- D. 25 m/s
Answer: 20 m/s
To convert km/h to m/s, multiply by 5/18: 72 × 5/18 = 20 m/s. To convert m/s back to km/h, multiply by 18/5 (20 × 18/5 = 72).
6. A train 150 m long is running at 54 km/h. How long will it take to pass a pole?
- A. 9 seconds
- B. 10 seconds
- C. 12 seconds
- D. 15 seconds
Answer: 10 seconds
Speed = 54 × 5/18 = 15 m/s, and to pass a pole the train must cover its own length, so time = 150 ÷ 15 = 10 seconds. To cross a platform, the train must cover its own length plus the platform's length.
7. A person travels from A to B at 40 km/h and returns from B to A at 60 km/h. What is the average speed for the whole journey?
- A. 48 km/h
- B. 50 km/h
- C. 52 km/h
- D. 45 km/h
Answer: 48 km/h
For equal distances, average speed = 2xy/(x + y) = (2 × 40 × 60)/(40 + 60) = 4800/100 = 48 km/h. Check with a distance of 120 km each way: 3 h + 2 h = 5 h for 240 km, and 240 ÷ 5 = 48; the answer is not 50 because more time is spent at the slower speed.
8. A number is first increased by 20% and then decreased by 20%. What is the net change?
- A. No change
- B. 2% decrease
- C. 4% increase
- D. 4% decrease
Answer: 4% decrease
Take the number as 100: after a 20% increase it becomes 120, and a 20% decrease of 120 is 24, giving 96, a net 4% decrease. Using the formula a + b + ab/100 = 20 − 20 + (20 × −20)/100 = −4%.
9. At what rate of simple interest per annum will a sum of money double itself in 8 years?
- A. 10%
- B. 12.5%
- C. 15%
- D. 8%
Answer: 12.5%
For the sum to double, the interest must equal the principal P, so P = (P × R × 8)/100, giving R = 100/8 = 12.5%. In general, the rate needed to double a sum at simple interest in T years is 100/T %.
10. The ages of A and B are in the ratio 3 : 4, and the sum of their ages is 56 years. What is B's age?
- A. 24 years
- B. 28 years
- C. 32 years
- D. 36 years
Answer: 32 years
Total parts = 3 + 4 = 7, so one part = 56 ÷ 7 = 8 years. B's age = 4 × 8 = 32 years and A's age = 3 × 8 = 24 years (check: 24 + 32 = 56).