NTS Quantitative Reasoning: Arithmetic — Questions and Answers
Question 1: A shopkeeper offers a 20% discount on an item marked at Rs. 500. What is the selling price?
- Rs. 350
- Rs. 380
- Rs. 400 (Correct answer)
- Rs. 420
Correct answer: Rs. 400
Discount = 20% of 500 = Rs. 100. Selling price = 500 - 100 = Rs. 400.
Discount amount = 20% × Rs. 500 = (20/100) × 500 = Rs. 100. Selling price = Marked price - Discount = Rs. 500 - Rs. 100 = Rs. 400. Alternatively, selling price = 80% × 500 = Rs. 400. Discount and profit/loss calculations are among the most common NTS arithmetic questions.
Question 2: If 8 apples cost Rs. 200, what is the cost of 5 apples?
- Rs. 100
- Rs. 115
- Rs. 125 (Correct answer)
- Rs. 130
Correct answer: Rs. 125
Cost per apple = 200/8 = Rs. 25. Cost of 5 apples = 25 × 5 = Rs. 125.
Unit price = Total cost / Number of items = Rs. 200 / 8 = Rs. 25 per apple. Cost of 5 apples = 5 × Rs. 25 = Rs. 125. This is a direct proportion problem (more apples = more cost). Unitary method and proportion problems are staples of NTS arithmetic.
Question 3: What is 3/5 expressed as a percentage?
- 50%
- 55%
- 60% (Correct answer)
- 65%
Correct answer: 60%
3/5 = (3/5) × 100% = 60%.
To convert a fraction to percentage, multiply by 100: (3/5) × 100 = 300/5 = 60%. Alternatively, 3 ÷ 5 = 0.6, and 0.6 × 100 = 60%. Converting between fractions, decimals, and percentages is a fundamental NTS arithmetic skill.
Question 4: A car travels at 80 km/h. How long will it take to cover 320 km?
- 3 hours
- 3.5 hours
- 4 hours (Correct answer)
- 4.5 hours
Correct answer: 4 hours
Time = Distance / Speed = 320 / 80 = 4 hours.
Using the speed-distance-time formula: Time = Distance / Speed = 320 km / 80 km/h = 4 hours. The three related formulas are: Speed = Distance/Time, Distance = Speed × Time, Time = Distance/Speed. These problems are very common in NTS quantitative reasoning.
Question 5: What is the average of 15, 20, 25, 30, and 35?
- 20
- 23
- 25 (Correct answer)
- 27
Correct answer: 25
Average = Sum/Count = (15+20+25+30+35)/5 = 125/5 = 25.
Sum = 15 + 20 + 25 + 30 + 35 = 125. Count = 5 numbers. Average = 125/5 = 25. Quick observation: these are 5 equally spaced numbers, so the average equals the middle number (25). This shortcut works for any arithmetic sequence. Average calculation is a basic NTS arithmetic skill.
Question 6: If the HCF of two numbers is 12 and their LCM is 144, and one number is 36, what is the other number?
- 36
- 42
- 48 (Correct answer)
- 54
Correct answer: 48
Product of two numbers = HCF × LCM. So other number = (12 × 144) / 36 = 48.
The fundamental relationship: HCF × LCM = Product of two numbers. Given HCF = 12, LCM = 144, and one number = 36. Product = 12 × 144 = 1,728. Other number = 1,728 / 36 = 48. Verification: HCF(36, 48) = 12 and LCM(36, 48) = 144. HCF and LCM relationships are commonly tested in NTS arithmetic.
Question 7: A father is 4 times as old as his son. If the son is 8 years old, how old will the father be in 5 years?
- 33
- 35
- 37 (Correct answer)
- 40
Correct answer: 37
Father's current age = 4 × 8 = 32. In 5 years: 32 + 5 = 37.
Son's current age = 8 years. Father's current age = 4 × 8 = 32 years. Father's age in 5 years = 32 + 5 = 37 years. Age problems involving ratios and future/past ages are very common in NTS arithmetic sections. Always establish current ages before calculating future or past ages.
Question 8: What is the square root of 196?
- 12
- 13
- 14 (Correct answer)
- 15
Correct answer: 14
√196 = 14, because 14 × 14 = 196.
√196 = 14, since 14² = 14 × 14 = 196. To estimate: 10² = 100, 15² = 225, so √196 is between 10 and 15. Testing: 13² = 169 (too small), 14² = 196 (correct). Perfect squares and their roots are basic NTS arithmetic knowledge.
Question 9: If a dozen eggs cost Rs. 240, what is the cost of 3 eggs?
- Rs. 50
- Rs. 55
- Rs. 60 (Correct answer)
- Rs. 70
Correct answer: Rs. 60
Cost per egg = 240/12 = Rs. 20. Cost of 3 eggs = 20 × 3 = Rs. 60.
A dozen = 12 items. Cost per egg = Rs. 240 / 12 = Rs. 20. Cost of 3 eggs = 3 × Rs. 20 = Rs. 60. This is a simple unitary method problem: find the unit cost, then multiply by the required quantity. Unitary method is a fundamental NTS arithmetic concept.
Question 10: A tank is 1/3 full. After adding 40 liters, it becomes 2/3 full. What is the total capacity of the tank?
- 100 liters
- 110 liters
- 120 liters (Correct answer)
- 130 liters
Correct answer: 120 liters
40 liters = 2/3 - 1/3 = 1/3 of the tank. Total capacity = 40 × 3 = 120 liters.
The amount added (40 liters) equals the difference between 2/3 and 1/3 of the tank capacity: 2/3 - 1/3 = 1/3. So 1/3 of capacity = 40 liters. Total capacity = 40 × 3 = 120 liters. Verification: 1/3 of 120 = 40 liters, 2/3 of 120 = 80 liters, difference = 40 liters. Fraction-based word problems are standard NTS fare.
Question 11: What number is 30% of 250?
- 65
- 70
- 75 (Correct answer)
- 80
Correct answer: 75
30% of 250 = (30/100) × 250 = 75.
30% of 250 = (30/100) × 250 = 0.30 × 250 = 75. Quick method: 10% of 250 = 25, so 30% = 3 × 25 = 75. Percentage calculations are among the most frequently tested topics in NTS arithmetic sections.
Question 12: Three friends share a bill of Rs. 2,700 in the ratio 2:3:4. How much does the friend with the largest share pay?
- Rs. 900
- Rs. 1,000
- Rs. 1,100
- Rs. 1,200 (Correct answer)
Correct answer: Rs. 1,200
Total parts = 2+3+4 = 9. Largest share = (4/9) × 2700 = Rs. 1,200.
Total ratio parts = 2 + 3 + 4 = 9. Value of one part = Rs. 2,700 / 9 = Rs. 300. Shares: First friend = 2 × 300 = Rs. 600, Second = 3 × 300 = Rs. 900, Third = 4 × 300 = Rs. 1,200. Verification: 600 + 900 + 1,200 = 2,700. Ratio and proportion problems are core NTS arithmetic topics.
