RRB NTPC Arithmetic and Number Systems 1 — Questions and Answers

Question 1: A train 150 m long passes a pole in 15 seconds. What is the speed of the train in km/h?

30 km/h
36 km/h (Correct answer)
40 km/h
45 km/h

Correct answer: 36 km/h

Speed = Distance/Time = 150/15 = 10 m/s. Converting to km/h: 10 × 18/5 = 36 km/h.

When a train passes a stationary object (pole), the distance covered equals the length of the train. Speed = Distance / Time = 150 m / 15 s = 10 m/s. To convert m/s to km/h, multiply by 3600/1000 = 18/5. Therefore, Speed = 10 × 18/5 = 36 km/h. This type of question frequently appears in RRB NTPC exams. Remember: m/s × (18/5) = km/h, and km/h × (5/18) = m/s.

Question 2: The LCM of 12, 18, and 24 is:

36
48
72 (Correct answer)
144

Correct answer: 72

LCM of 12, 18, 24: Prime factorize: 12=2²×3, 18=2×3², 24=2³×3. LCM = 2³×3² = 8×9 = 72.

To find LCM of 12, 18, and 24: Prime factorization: 12 = 2² × 3¹, 18 = 2¹ × 3², 24 = 2³ × 3¹. LCM takes the highest power of each prime factor: LCM = 2³ × 3² = 8 × 9 = 72. Verification: 72/12=6 ✓, 72/18=4 ✓, 72/24=3 ✓. LCM is commonly tested in RRB NTPC along with HCF. Remember: HCF × LCM = Product of two numbers (for two numbers only).

Question 3: If the simple interest on a sum for 2 years at 5% per annum is Rs. 400, what is the principal?

Rs. 2000
Rs. 3000
Rs. 4000 (Correct answer)
Rs. 4500

Correct answer: Rs. 4000

SI = PRT/100 → 400 = P×5×2/100 → P = 400×100/10 = Rs. 4000.

Simple Interest formula: SI = (P × R × T) / 100, where P = Principal, R = Rate of interest per annum, T = Time in years. Given: SI = Rs. 400, R = 5%, T = 2 years. Substituting: 400 = (P × 5 × 2) / 100 → 400 = 10P/100 → 400 = P/10 → P = 400 × 10 = Rs. 4,000. Verification: SI = (4000 × 5 × 2)/100 = 40000/100 = Rs. 400 ✓. This is a fundamental formula for RRB NTPC quantitative aptitude.

Question 4: What is 15% of 480?

60
62
72 (Correct answer)
75

Correct answer: 72

15% of 480 = (15/100) × 480 = 15 × 4.8 = 72.

To calculate 15% of 480: Method 1: (15/100) × 480 = 15 × 4.8 = 72. Method 2 (mental math): 10% of 480 = 48; 5% of 480 = 24; 15% = 10% + 5% = 48 + 24 = 72. Percentage calculations are extremely common in RRB NTPC. Practice both the direct method and the mental math decomposition method for speed. Common percentages to memorize: 25% = 1/4, 33.33% = 1/3, 50% = 1/2, 66.67% = 2/3, 75% = 3/4.

Question 5: A number when divided by 6 leaves a remainder of 3. What will be the remainder when the same number is divided by 3?

0 (Correct answer)
1
2
3

Correct answer: 0

If N = 6q + 3, then N = 3(2q+1), so N is exactly divisible by 3, leaving remainder 0.

If a number N leaves remainder 3 when divided by 6, then N can be written as: N = 6q + 3 (where q is the quotient). Factoring: N = 6q + 3 = 3(2q) + 3 = 3(2q + 1). Since N = 3 × (2q+1), N is completely divisible by 3, leaving remainder 0. This can also be verified with an example: N = 9 (= 6×1 + 3). 9 ÷ 6 = 1 remainder 3 ✓; 9 ÷ 3 = 3 remainder 0 ✓. Key insight: Since 3 is a factor of 6, any remainder when divided by 6 that is divisible by 3 will give remainder 0 when divided by 3.

Question 6: The ratio of the ages of A and B is 3:5. If the sum of their ages is 64 years, what is B's age?

24 years
30 years
34 years
40 years (Correct answer)

Correct answer: 40 years

Let ages be 3x and 5x. Then 3x + 5x = 64 → 8x = 64 → x = 8. B's age = 5x = 5×8 = 40 years.

Let A's age = 3x and B's age = 5x (maintaining the ratio 3:5). Sum of ages: 3x + 5x = 64 → 8x = 64 → x = 8. Therefore: A's age = 3 × 8 = 24 years; B's age = 5 × 8 = 40 years. Verification: A:B = 24:40 = 3:5 ✓; A+B = 24+40 = 64 ✓. Ratio problems are common in RRB NTPC. The key technique is to assign a variable multiplier (x) to each part of the ratio, then use the given total to solve for x.

RRB NTPC Arithmetic and Number Systems 1

A train 150 m long passes a pole in 15 seconds.
What is the speed of the train in km/h?