CRPF Radio Operator, Cipher & Radio Fitter Exam | Previous Year Math Questions & Solutions

Previous Year Math Questions & Solutions: The CRPF (Central Reserve Police Force) Radio Operator, Cipher, and Radio Fitter Exam is one of the most competitive recruitment tests for candidates aspiring to join the paramilitary forces in technical roles. A strong grasp of Mathematics is crucial for success in this exam, as it plays a significant role in the selection process.

computer for crpf radio operator , cipher and radio fiter | mathmetics | computer |previous year question paper

In this article, we will cover:
✅ The importance of mathematics in the CRPF exam
✅ Key topics from previous years’ math papers
✅ Sample questions with solutions
✅ Tips to improve your mathematical skills

Importance of Mathematics in CRPF Radio Operator, Cipher & Radio Fitter Exam

Mathematics is a fundamental part of the CRPF technical recruitment process. It helps assess a candidate’s problem-solving abilities, logical reasoning, and analytical skills. The Mathematical Aptitude section in the exam typically includes questions from:
🔹 Arithmetic – Number System, Percentage, Profit & Loss, Time & Work
🔹 Algebra – Equations, Polynomials, Simplifications
🔹 Geometry & Mensuration – Area, Volume, Perimeter Calculations
🔹 Trigonometry – Basic identities, Heights & Distances
🔹 Data Interpretation – Charts, Graphs, Tables

Previous Year Math Questions with Solutions

Here are some important questions from previous CRPF Radio Operator, Cipher, and Radio Fitter exams:

1. Number System Question

📝 Q1: Find the smallest number that is divisible by both 12 and 18.
💡 Solution: The LCM of 12 and 18 is 36. So, the smallest number is 36.

2. Percentage Question

📝 Q2: A candidate scores 320 marks out of 400. What is his percentage?
💡 Solution: (320/400) × 100 = 80%

3. Profit & Loss Question

📝 Q3: A radio was bought for ₹3,000 and sold for ₹3,600. Find the profit percentage.
💡 Solution:
Profit = Selling Price – Cost Price = ₹3,600 – ₹3,000 = ₹600
Profit % = (600/3000) × 100 = 20%

4. Time & Work Question

📝 Q4: A and B can complete a task in 10 days and 15 days, respectively. How long will they take to finish it together?
💡 Solution:
A’s one-day work = 1/10, B’s one-day work = 1/15
Total work per day = (1/10 + 1/15) = 1/6
So, they will complete the task in 6 days.

5. Trigonometry Question

📝 Q5: If sin 30° = ?
💡 Solution: sin 30° = 1/2

Preparation Tips for CRPF Math Section

📌 Practice Previous Year Papers – Solve past questions to understand the pattern.
📌 Improve Speed & Accuracy – Use shortcuts for calculations.
📌 Revise Important Formulas – Keep a formula sheet handy.
📌 Take Mock Tests – Attempt regular tests to assess your performance.

CRPF Radio Operator, Cipher & Radio Fitter Exam | Previous Year Math Questions & Solutions

Here is the proper question-answer format with the first question serial number as 1 and the correct answer provided below each question:

1. 55 ÷ 5.5 – 0.5 = ?
a) 9.5
b) 10
c) 8.5
d) 10.5
Answer: a) 9.5

2. If 20% of a = 40% of b, then a : b = ?
a) 2:3
b) 3:2
c) 1:3
d) 2:1
Answer: d) 2:1

3. 4 × ? = 4062 ÷ 5
a) 205.1
b) 203.1
c) 213.1
d) 215.1
Answer: b) 203.1

4. If √4n = 256, then n is:
a) 2
b) 4
c) 6
d) 8
Answer: d) 8

5. (16% of 550) ÷ (Y% of 500) = 2.5, then Y equals to:
a) 5.64
b) 8.11
c) 7.04
d) 6.08
Answer: c) 7.04

6. The average of even numbers from 1 to 20 is:
a) 12
b) 11
c) 10
d) 110
Answer: a) 12

7. 26 × 23 ÷ 24 = 2x, then x is equal to:
a) 2
b) 3
c) 5
d) 7
Answer: c) 5

8. How many prime factors are there in the prime factorisation of 5005?
a) 2
b) 4
c) 6
d) 7
Answer: b) 4

9. If (2/x) + (3/y) = 13 and (5/x) – (4/y) = -2, then x and y are:
a) 2, 1/3
b) 1/2, 3
c) 2, 3
d) 1/2, 1/3
Answer: b) 1/2, 3

10. (Sec A + Tan A)(1 – Sin A) = ?
a) Sec A
b) Cos A
c) Sin A
d) Cosec A
Answer: b) Cos A

11. The angle of elevation of the top of a tower from a point on the ground, which is 30 meters away from the foot of the tower, is 30°. The height of the tower is:
a) 30√3 meters
b) 10 meters
c) 10√3 meters
d) 10/√3 meters
Answer: c) 10√3 meters

12. The sum of 15% of a positive number and 10% of the same number is 70. What is twice of that number?
a) 440
b) 280
c) 560
d) 140
Answer: c) 560

13. What would be the simple interest accrued in four years on a principal of Rs. 18,440 at the rate of 15% per annum?
a) Rs. 11,075
b) Rs. 12,205
c) Rs. 11,500
d) Rs. 11,064
Answer: d) Rs. 11,064

14. A box contains 3 blue, 2 white, and 4 red marbles. If a marble is drawn at random from the box, the probability that it will be blue is:
a) 1/3
b) 1/2
c) 2/3
d) 1
Answer: a) 1/3

15. Point (-10, 0) lies:
a) on the negative direction of the x-axis
b) on the negative direction of the y-axis
c) in the third quadrant
d) in the fourth quadrant
Answer: a) on the negative direction of the x-axis

16. Mohan bought a cycle for Rs. 475 and then sold it at a loss of 8% of the cost price. For how much did he sell the cycle?
a) Rs. 453
b) Rs. 419
c) Rs. 441
d) Rs. 437
Answer: d) Rs. 437

17. (√3 + √5)² + (√3 – √5)² = ?
a) -4
b) 2(√3 – √5)
c) 16
d) 2(√3 + √5)
Answer: c) 16

18. Find the least number that is exactly divisible by 8, 12, and 36.
a) 72
b) 36
c) 18
d) 44
Answer: a) 72

19. A person crosses a 400-meter-long street in 8 minutes. The speed of that person in km/hr is:
a) 5
b) 0.6
c) 3.2
d) 3
Answer: d) 3

20. (5π/3) radian = ?
a) 150°
b) 300°
c) 600°
d) 200°
Answer: b) 300°

Here is the proper question-answer format starting with serial number 20, and the correct answer is provided below each question:

20. 5454 ÷ 54 ÷ 5 = ?
a) 15.3
b) 25.5
c) 30.5
d) 20.2
Answer: d) 20.2

21. 22% of 364 – ? = 23
a) 50.2
b) 57.8
c) 53.6
d) None of these
Answer: b) 57.8

22. √? – 5 = √2209
a) (52)²
b) √52
c) 52
d) None of these
Answer: a) (52)²

23. Complete the series: 5, ?, 15, 75, 525, 4725, 51975
a) 5
b) 10
c) 6
d) 8
Answer: a) 5

24. The average weight of 21 boys was recorded as 64 kg. If the weight of the teacher was added, the average increased by one kg. What was the teacher’s weight?
a) 64 kg
b) 86 kg
c) 72 kg
d) 98 kg
Answer: b) 86 kg

25. The perimeter of a square is twice the perimeter of a rectangle. If the perimeter of the square is 72 cm and the length of the rectangle is 12 cm, what is the difference between the breadth of the rectangle and the side of the square?
a) 9 cm
b) 18 cm
c) 12 cm
d) 3 cm
Answer: a) 9 cm

26. A truck covers a distance of 640 km in 10 hours. A car covers the same distance in 8 hours. What is the respective ratio between the speed of the truck and the car?
a) 3:4
b) 1:2
c) 5:6
d) None of these
Answer: a) 3:4

27. The respective ratio between Sita’s, Riya’s, and Kunal’s monthly income is 84:76:89. If the annual income is Rs. 456000, what is the sum of Sita’s and Kunal’s annual income?
a) Rs. 1195000
b) Rs. 983500
c) Rs. 1038000
d) Rs. 1130000
Answer: c) Rs. 1038000

28. The sum of 15% of a positive number and 20% of the same number is 126. What is one-third of that number?
a) 120
b) 1080
c) 360
d) 40
Answer: a) 120

29. Neeraj incurred a loss of 55% on selling an article for Rs. 9549. What was the cost price of the article?
a) Rs. 27700
b) Rs. 25600
c) Rs. 21220
d) Rs. 29000
Answer: c) Rs. 21220

30. In how many different ways can the letters of the word “VENTURE” be arranged?
a) 840
b) 5040
c) 1260
d) 2520
Answer: d) 2520

31. In order to pass in an exam, a student is required to get 780 marks out of the aggregate marks. Sonu got 728 marks and was declared failed by 5%. What are the maximum aggregate marks a student can get in the examination?
a) 1040
b) 1100
c) 560
d) 1400
Answer: a) 1040

32. Harish, Dilip, and Asha start running around a circular stadium and complete one round in 27s, 9s, and 36s respectively. In how much time will they meet again at the starting point?
a) 2 min 36 s
b) 1 min 48 s
c) 3 min 11 s
d) 2 min 25 s
Answer: b) 1 min 48 s

33. 15 years hence, Priya will be just four times as old as she was 15 years ago. Her present age is:
a) 25 years
b) 15 years
c) 40 years
d) 35 years
Answer: a) 25 years

34. Rajan and Sajan started a business initially with Rs. 14200 and Rs. 15600, respectively. If the total profit is Rs. 74500, what is Rajan’s share in the profit?
a) Rs. 39000
b) Rs. 39600
c) Rs. 35000
d) Rs. 35500
Answer: d) Rs. 35500

35. A sum of money doubles itself in 8 years at simple interest. What is the rate of interest?
a) 12.5%
b) 12.8%
c) 12.9%
d) None of these
Answer: a) 12.5%

36. A and B take Rs. 660 for doing a piece of work together. If working alone, A and B take 6 days and 5 days, respectively. A’s share is:
a) Rs. 400
b) Rs. 420
c) Rs. 300
d) Rs. 560
Answer: c) Rs. 300

37. A train 270 m long passes a standing man in 24 s. What is the speed of the train?
a) 45 km/h
b) 40.5 km/h
c) 20 km/h
d) 20.5 km/h
Answer: b) 40.5 km/h

38. If the length of a rectangle is increased by 40% and the breadth is reduced by 20%, what will be the effect on its area?
a) Increased by 8%
b) Increased by 20%
c) Increased by 12%
d) Increased by 16%
Answer: c) Increased by 12%

39. In how much time will a man cover a distance of 4500 m with a speed of 15 km/h?
a) 10 min
b) 18 min
c) 24 min
d) 16 min
Answer: b) 18 min

Here is the proper question-answer format starting with serial number 40, and the correct answer is provided below each question:

40. If the area of a circle is decreased by 36%, then the radius of the circle is decreased by:
a) 20%
b) 18%
c) 36%
d) 64%
Answer: a) 20%

41. The floor of a rectangular room is 15m long and 12m wide. The room is surrounded by a verandah of width 2m on all its sides. The area of the verandah is:
a) 124 m²
b) 120 m²
c) 108 m²
d) 158 m²
Answer: a) 124 m²

42. The area of a triangle is 615 m². If one of its sides is 123 m, find the length of the perpendicular dropped on that side from the opposite vertex.
a) 15 m
b) 12 m
c) 10 m
d) 18 m
Answer: c) 10 m

43. A car covers a distance of 540 km in 9 hours. The speed of a train is double the speed of the car. Two-thirds the speed of the train is equal to the speed of a bike. How much distance will the bike cover in 5 hours?
a) 450 km
b) 360 km
c) 400 km
d) 500 km
Answer: c) 400 km

44. A man starts from B to K and another from K to B at the same time. After passing each other, they complete their journeys in 3⅓ and 4⅘ hours, respectively. Find the speed of the second man if the speed of the first is 12 kmph.
a) 12.5 kmph
b) 10 kmph
c) 12.66 kmph
d) 20 kmph
Answer: b) 10 kmph

45. Three taps A, B, and C can fill a tank in 12, 15, and 20 hours, respectively. If A is open all the time and B and C are open for one hour each alternately, then the tank will be full in:
a) 6 hours
b) 6⅔ hours
c) 7 hours
d) 7⅓ hours
Answer: c) 7 hours

46. A is 30% more efficient than B. How much time will they, working together, take to complete a job which A alone could have done in 23 days?
a) 11 days
b) 13 days
c) 20 days
d) None of these
Answer: b) 13 days

47. Computer A takes 3 minutes to process an input, while Computer B takes 5 minutes. If Computers A, B, and C can process an average of 14 inputs in one hour, how many minutes does Computer C alone take to process one input?
a) 10
b) 4
c) 6
d) 8
Answer: c) 6

48. The ratio of the ages of A and B seven years ago was 3:4, respectively. The ratio of their ages nine years from now will be 7:8, respectively. What is B’s age at present?
a) 16 years
b) 19 years
c) 28 years
d) 23 years
Answer: d) 23 years

49. The largest and second-largest angles of a triangle are in the ratio of 13:12. The smallest angle is 20% of the sum of the largest and second-largest angles. What is the sum of the smallest and the second-largest angles?
a) 120°
b) 108°
c) 100°
d) 102°
Answer: d) 102°

50. The total of the ages of a class of 75 girls is 1050. The average age of 25 of them is 12 years, and that of another 25 is 16 years. Find the average age of the remaining girls.
a) 12 years
b) 13 years
c) 14 years
d) 15 years
Answer: c) 14 years

51. The average of 5 consecutive even numbers A, B, C, D, and E is 52. What is the product of B and E?
a) 2916
b) 2988
c) 3000
d) 2800
Answer: d) 2800

52. Mohan bought a jute bag at a 30% discount on the list price. He then sold it at a price that was 160% of the list price, thereby making a profit of Rs. 81. What is the list price of the bag?
a) 90
b) 100
c) 180
d) 200
Answer: c) 180

53. A man sold two articles at Rs. 375 each. On one, he gains 25%, and on the other, he loses 25%. The gain or loss on the whole transaction is:
a) 6%
b) 6.25%
c) Rs. 50
d) 6.75%
Answer: b) 6.25%

54. The profit percent of a bookseller if he sells a book at the marked price after enjoying a commission of 25% on the marked price will be:
a) 30%
b) 25%
c) 20%
d) 33.33%
Answer: d) 33.33%

55. What will be the difference between the compound interest and simple interest at the rate of 5% p.a. on an amount of Rs. 4000 at the end of two years?
a) 10
b) 20
c) 30
d) Data inadequate
Answer: a) 10

56. Rahul has borrowed Rs. 20,000 from two money lenders. On one, he had to pay 8% p.a. S.I. per year, and on the other amount, he had to pay 12% p.a. S.I. After 3 years, he paid a total interest of Rs. 5760. Find the amount borrowed at 12% p.a.
a) 12,000
b) 8,000
c) 5,000
d) 10,000
Answer: b) 8,000

57. 71% of a number is more than its 46% by 120. What is 30% of that number?
a) 160
b) 150
c) 144
d) 148
Answer: c) 144

58. √? + 17 = √961
a) 169
b) 256
c) 225
d) 196
Answer: d) 196

59. What is the least number to be added to 3986 to make it a perfect square?
a) 118
b) 95
c) 110
d) 100
Answer: c) 110

Here is the proper question-answer format starting with serial number 60, and the correct answer is provided below each question:

60. 6, 42, 294, 2058, 14406, ?
a) 100842
b) 72030
c) 129654
d) 115248
Answer: a) 100842

61. 13, 20, 14, 19, 15, ?
a) 16
b) 18
c) 21
d) 17
Answer: b) 18

62. 2, 16, 112, 672, 3360, 13440, ?
a) 43240
b) 3430
c) 3340
d) 40320
Answer: d) 40320

63. 7825 – 9236 + 5234 = ? * 25
a) 152.92
b) 152.29
c) 125.92
d) 125.29
Answer: a) 152.92

64. 5, 13, 25, 41, ?, 85, 113
a) 64
b) 68
c) 61
d) 36
Answer: c) 61

65. The product of two relative prime numbers is 143. Find their HCF.
a) 3
b) 9
c) 13
d) 1
Answer: d) 1

66. The least number which, when divided by 9, 11, and 15, leaves the same remainder in each case, is:
a) 495
b) 503
c) 530
d) 580
Answer: b) 503

67. Find the least number that is exactly divisible by 8, 12, and 36.
a) 36
b) 18
c) 36
d) 72
Answer: d) 72

68. Which is the greatest number that will divide 1600 and 1420 exactly?
a) 10
b) 15
c) 20
d) 25
Answer: c) 20

69. In a school, all the students can stand in a row so that each row has 5, 9, or 10 students. Find the least number of students in the school.
a) 90
b) 95
c) 85
d) 100
Answer: a) 90

70. The sum of two numbers is 10, and their product is 20. The sum of the reciprocals of the two numbers is:
a) 1
b) 3/5
c) 1/2
d) 11/6
Answer: c) 1/2

71. Find the sum of all even natural numbers up to 74.
a) 1518
b) 1471
c) 1618
d) 1406
Answer: a) 1518

72. 51% of a number is 714. What is 28% of that number?
a) 378
b) 392
c) 351
d) 364
Answer: b) 392

73. The sum of the first 20 odd natural numbers is equal to:
a) 400
b) 300
c) 420
d) 210
Answer: a) 400

74. If 3 4 a 6 8 is to be divisible by 9, the value of the missing digit, a, should be:
a) 5
b) 8
c) 7
d) 6
Answer: d) 6

75. Two-thirds of 10% of 60% of A is 32. Find the value of A.
a) 750
b) 600
c) 800
d) 900
Answer: c) 800

76. The price of a computer is Rs. 20,000. What will be the price of the computer after a reduction of 25%?
a) 12,000
b) 15,000
c) 21,000
d) 18,000
Answer: b) 15,000

77. 46% of 156 – 23.76 = ?
a) 48
b) 48.10
c) 47
d) 47.10
Answer: a) 48

78. (12.999)³ = ?
a) 1800
b) 2000
c) 2200
d) 1500
Answer: c) 2200

79. 940.9 + 9.9 + 90.09 + 99.9999 = ?
a) 1141.699
b) 1230.799
c) 294.88
d) 1140.889
Answer: d) 1140.889

Here is the proper question-answer format starting with serial number 80, and the correct answer is provided below each question:

80. 22/7 is a:
a) Real number
b) Rational number
c) Irrational number
d) Composite number
Answer: b) Rational number

81. A rectangular field is surrounded on all sides by a 1 m pathway. The length and breadth of the field are 60 m and 40 m, respectively. Find the area of the pathway.
a) 204 sqm
b) 208 sqm
c) 210 sqm
d) 216 sqm
Answer: a) 204 sqm

82. The sum of all the angles of an octagon is:
a) 900°
b) 980°
c) 1080°
d) 1200°
Answer: c) 1080°

83. From a deck of 52 cards, we draw 2 cards one by one without replacement. Find the probability that both cards are Aces.
a) 1/103
b) 1/104
c) 1/221
d) 1/241
Answer: c) 1/221

84. Sin90° × Sin30° =
a) 1/2
b) 1/4
c) 1/2.5
d) 1
Answer: a) 1/2

85. A man buys an article for Rs. 27.50 and sells it for Rs. 28.60. Find his gain percent.
a) 1%
b) 2%
c) 3%
d) 4%
Answer: d) 4%

86. A clock strikes once at 1 o’clock, twice at 2 o’clock, thrice at 3 o’clock, and so on. How many times will it strike in 24 hours?
a) 78
b) 136
c) 156
d) 196
Answer: c) 156

87. The average of the first 50 natural numbers is:
a) 25.30
b) 25.5
c) 25.00
d) 12.25
Answer: b) 25.5

88. Which of the following numbers gives 240 when added to its own square?
a) 15
b) 16
c) 18
d) 20
Answer: a) 15

89. How many surfaces are there in a cube?
a) 3
b) 4
c) 5
d) None of these
Answer: d) None of these (A cube has 6 surfaces.)

90. What should be added to 53/7 to get 12?
a) 7/25
b) 9/34
c) 2/59
d) 46/7
Answer: d) 46/7

91. Two numbers are in the ratio 4:5. If the sum of the numbers is 135, find the numbers.
a) 60 and 75
b) 50 and 65
c) 70 and 95
d) 65 and 75
Answer: a) 60 and 75

92. A car can cover a distance of 522 km on 36 liters of petrol. How far can it travel on 14 liters of petrol?
a) 213 km
b) 223 km
c) 203 km
d) 302 km
Answer: c) 203 km

93. The square root of 0.0081 is:
a) 0.09
b) 0.9
c) 0.91
d) 0.009
Answer: a) 0.09

94. All natural numbers and 0 are called the:
a) Whole numbers
b) Prime numbers
c) Integers
d) Rational numbers
Answer: a) Whole numbers

95. The wages of 10 workers for a six-day week is Rs. 1200. What will be the one day’s wage of 4 workers?
a) Rs. 40
b) Rs. 32
c) Rs. 80
d) Rs. 24
Answer: c) Rs. 80

96. If cos A = 4/5, then tan A =
a) 3/5
b) 3/4
c) 4/3
d) 5/3
Answer: b) 3/4

97. Ram cycles at a constant speed of 10 km/hr and reaches his school on time. If he cycles at a constant speed of 15 km/hr, he reaches his school 12 minutes early. The distance of the school is _ kms.
a) 4
b) 6
c) 9
d) 12
Answer: b) 6

98. Find the missing number in the series: 5, 12, __, 54, 110.
a) 26
b) 24
c) 18
d) 20
Answer: a) 26

99. Kamal is 5 years older than Raj, who is thrice as old as Arun. If the sum of their ages is 40, how old is Raj?
a) 5
b) 10
c) 15
d) 20
Answer: c) 15

Conclusion

The CRPF Radio Operator, Cipher & Radio Fitter Exam demands a solid mathematical foundation. Regular practice, along with solving previous years’ papers, can significantly boost your chances of success. Focus on key topics like Arithmetic, Algebra, Trigonometry, and Data Interpretation to score well in the exam.

💡 Stay consistent, practice daily, and success will follow! 🚀💯

Let us know in the comments if you need more practice questions or guidance!

Would you like me to add anything else? 😊