RRB NTPC Arithmetic and Number Systems 2 — Questions and Answers

Question 1: A shopkeeper marks his goods 25% above cost price and gives a 10% discount. What is his profit percentage?

10%
12.5% (Correct answer)
15%
17.5%

Correct answer: 12.5%

Let CP = 100. MP = 125. SP = 125 × 0.9 = 112.5. Profit% = (112.5-100)/100 × 100 = 12.5%.

Let Cost Price (CP) = Rs. 100. Marked Price (MP) = CP + 25% of CP = 100 + 25 = Rs. 125. After 10% discount: Selling Price (SP) = MP - 10% of MP = 125 - 12.5 = Rs. 112.5. Profit = SP - CP = 112.5 - 100 = Rs. 12.5. Profit% = (Profit/CP) × 100 = (12.5/100) × 100 = 12.5%. Formula: If markup = m% and discount = d%, Net profit% = m - d - (m×d)/100. Here: 25 - 10 - (25×10)/100 = 25 - 10 - 2.5 = 12.5%.

Question 2: Find the value of: √(0.0081)

0.009
0.09 (Correct answer)
0.9
0.81

Correct answer: 0.09

√(0.0081) = √(81/10000) = √81/√10000 = 9/100 = 0.09.

√(0.0081) = √(81/10000). Since √81 = 9 and √10000 = 100: √(81/10000) = 9/100 = 0.09. Alternative method: Count the decimal places — 0.0081 has 4 decimal places, so its square root will have 2 decimal places. √81 = 9, so √0.0081 = 0.09. Verification: 0.09 × 0.09 = 0.0081 ✓. Square root questions are common in RRB NTPC. Key squares to memorize: √0.01 = 0.1, √0.04 = 0.2, √0.09 = 0.3, √0.16 = 0.4, √0.25 = 0.5.

Question 3: A boat travels 30 km upstream in 6 hours and 30 km downstream in 3 hours. What is the speed of the stream?

2.5 km/h (Correct answer)
3 km/h
2 km/h
5 km/h

Correct answer: 2.5 km/h

Upstream speed = 30/6 = 5 km/h; Downstream speed = 30/3 = 10 km/h. Stream speed = (Downstream - Upstream)/2 = (10-5)/2 = 2.5 km/h.

Upstream speed = Distance/Time = 30/6 = 5 km/h. Downstream speed = 30/3 = 10 km/h. In boat and stream problems: Downstream speed = Boat speed + Stream speed; Upstream speed = Boat speed - Stream speed. Therefore: Stream speed = (Downstream speed - Upstream speed) / 2 = (10 - 5) / 2 = 5/2 = 2.5 km/h. Boat speed (in still water) = (Downstream + Upstream) / 2 = (10 + 5) / 2 = 7.5 km/h.

Question 4: The difference between a two-digit number and the number obtained by interchanging its digits is 36. What is the difference between the digits?

2
4 (Correct answer)
6
8

Correct answer: 4

Let digits be a and b. Original number = 10a+b, reversed = 10b+a. Difference: (10a+b)-(10b+a) = 9(a-b) = 36 → a-b = 4.

Let the two-digit number have tens digit 'a' and units digit 'b'. Original number = 10a + b. Number with interchanged digits = 10b + a. Difference = (10a + b) - (10b + a) = 9a - 9b = 9(a - b). Given difference = 36: 9(a - b) = 36 → a - b = 4. This is a key property: the difference between any two-digit number and its digit-reverse is always a multiple of 9, specifically 9 × (difference between digits). This principle extends to larger numbers too.

Question 5: If A can do a piece of work in 10 days and B can do the same work in 15 days, how many days will they take together?

5 days
6 days (Correct answer)
7 days
8 days

Correct answer: 6 days

A's work per day = 1/10; B's work per day = 1/15. Together = 1/10 + 1/15 = 3/30 + 2/30 = 5/30 = 1/6. So they finish in 6 days.

Work done by A in one day = 1/10 of the total work. Work done by B in one day = 1/15 of the total work. Combined work per day = 1/10 + 1/15. Finding LCM of 10 and 15 = 30. 1/10 + 1/15 = 3/30 + 2/30 = 5/30 = 1/6. Together they complete 1/6 of the work per day, so they finish in 6 days. Formula: If A takes 'a' days and B takes 'b' days, together they take ab/(a+b) days = (10×15)/(10+15) = 150/25 = 6 days.

Question 6: What is the compound interest on Rs. 10,000 at 10% per annum for 2 years?

Rs. 1,900
Rs. 2,000
Rs. 2,100 (Correct answer)
Rs. 2,200

Correct answer: Rs. 2,100

CI = P[(1+r/100)^n - 1] = 10000[(1.1)² - 1] = 10000[1.21 - 1] = 10000 × 0.21 = Rs. 2,100.

Compound Interest = P(1 + R/100)ⁿ - P. Given: P = 10,000, R = 10%, n = 2 years. CI = 10,000 × (1 + 10/100)² - 10,000 = 10,000 × (1.1)² - 10,000 = 10,000 × 1.21 - 10,000 = 12,100 - 10,000 = Rs. 2,100. Year-by-year method: Year 1 interest = 10% of 10,000 = 1,000; New principal = 11,000. Year 2 interest = 10% of 11,000 = 1,100. Total CI = 1,000 + 1,100 = 2,100. Note: Simple Interest would have been Rs. 2,000 — CI is always greater than SI when n > 1.

RRB NTPC Arithmetic and Number Systems 2

A shopkeeper marks his goods 25% above cost price and gives a 10% discount.
What is his profit percentage?