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SSC CPO (SI Delhi Police & CAPF) Quantitative Aptitude — Previous Year Questions

730 Quantitative Aptitude questions asked in past SSC CPO (SI Delhi Police & CAPF) papers, split into 73 timed practice sets — every question with its answer and explanation.

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About SSC CPO (SI Delhi Police & CAPF) Quantitative Aptitude previous year questions

This page collects every Quantitative Aptitude question that has appeared in past SSC CPO (SI Delhi Police & CAPF) papers on AajExam — 730 questions in total, organised into 73 short, timed practice sets. Each question is shown with its four options, the correct answer, and an explanation of the reasoning, so you can use the page either as a self-test or as a revision reference. Why previous year questions are the highest-value Quantitative Aptitude preparation you can do for SSC CPO (SI Delhi Police & CAPF): recruitment boards reuse a stable pool of concepts across cycles. The wording changes, the underlying idea rarely does. Working through a few hundred genuine past Quantitative Aptitude questions teaches you which sub-topics the paper actually rewards, how the examiner likes to frame distractors, and roughly how long each question type should take — none of which a syllabus document can tell you. How to use this page: attempt questions in blocks of ten without looking at the answers, then review every question you got wrong or guessed. Read the explanation for the concept, not just the answer letter. When a concept keeps catching you out, open the related topic page linked below and drill that single area before returning here. Repeat across the full bank, and track how your accuracy on the second pass compares with your first — a 15-20% improvement is normal and is the clearest sign your preparation is working. What is in this bank: the questions are transcribed from actual SSC CPO (SI Delhi Police & CAPF) question papers, kept in the original order and wording, with solutions written by subject specialists. Sets are free to attempt, work on mobile, and need no login to read. If you would rather practise a complete paper end to end under exam conditions, the full SSC CPO (SI Delhi Police & CAPF) previous-year papers are linked below as well.

Quantitative Aptitude PYQs asked in SSC CPO (SI Delhi Police & CAPF)

A sample of 30 questions from the full bank of 730. Try each one before opening the solution — the remaining questions are in the timed practice sets below.

Q1.A truck goes from Haryana to Bangalore with an average speed of 60 km/h. The journey takes 30 hours. It returns from Bangalore to Haryana on the same road with an average speed of 40 km/h. What was the average speed of the truck during the roundtrip?
- A.60 km/h
- B.40 km/h
- C.50 km/h
- D.48 km/h
Show answer
Answer: C. 50 km/h
. Let total sales = x
Q2.In a journey of three unequal laps, a car covers a distance
- A.222 sin 
- B.2 cos 
- C.1 2 2 sin 
- D.1 cos 
Show answer
Answer: B. 2 cos 
. The LCM of 25, 30, 50 and 75. The LCM is 150 as 150 is divisible by all numbers viz. 25, 30, 50 and 75. Hence, 150 is the correct Answer.
Q3.2 of 200 km in 4 h in the first lap, while another 162 km at the speed of 15 m/s in the second lap. It covered the remaining distance of the final lap in 4 h such that the 60 men can complete a work in 40 days. They start work together but after every 10 day, 5 men leave the work. In how many days will the work be completed?
- A.47.5
- B.49.5
- C.42.5
- D.45.5
Show answer
Answer: A. 47.5
. 22cos θ + sin θ = cos θ 2 2 Squaring on both the sides, we get, Discount = 1 552 % 5 5 → cos2θ + sin2θ + 2 sin θ cos θ = 2 cos2θ → cos2θ – sin2θ = 2 cos θ sin θ And bonus = 1 % on his total sales. 2 → (cos θ + sin θ)(cos θ – sin θ) = 2 cos θ sin θ → 2cos (cos   sin )  2 cos  sin  1 0.5 → 5 2 %  x  100 x  10000  1990 cos θ – sin θ = 2 sin  5.5 0.5 0.5 Hence, 2 sin  is the correct
Q4.If the number 8764x5 is divisible by 9, then find the least possible value of x where x is a two–digit number.
- A.15
- B.06
- C.14
- D.18
Show answer
Answer: B. 06
. Marks in Chemistry = 90 + 75 + 65 + 85 + 95 + 90 = 500 Geography = 80 + 85 + 95 + 95 + 95 + 90 = 540 Marks in History = 70 + 85 + 90 + 90 + 90 + 90 = 515 Marks in CS = 95 + 90 + 80 + 85 + 80 + 90 = 520 Hence, marks are highest in Geography which is 540.
Q5.Find the HCF of 364 and 724.
- A.4
- B.2
- C.6
- D.364
Show answer
Answer: A. 4
. We know that curved surface area of cylinder = 2mrh → 2mrh = 1388 cm2 → 2m21 × r = 1388 cm2
Q6.If a, b, c are all non-zero and a + b + c = 0, find the value a2  b2  c2 . average speed of the car for entire journey was 50 km/h. What was the speed of the car in the third lap of the journey?
- A.47 km/h
- B.52 km/h
- C.42 km/h
- D.45 km/h
Show answer
Answer: A. 47 km/h
. Total work = 60 × 40 = 2400 Work completed in first 10 days = 10 × 60 = 600 Work in the next 10 days = 55 × 10 = 550 Work in the next 10 days = 50 × 10 = 500 Work in the 10 days = 45 × 10 = 450 Total work done in 40 days = 2100 Remaining work is 2400 – 2100 = 300 Therefore only 40 men has to do 300 work, so days they will take = 300  7.5 days 40 Hence, 47.5 days is the correct Answer.
Q7.Three persons P, Q, R run along a circular track at speeds of 3 km/h, 4 km/h, 6 km/h, respectively. If the length of the track is 36 km, then after how much time will they meet again at the starting point?
- A.38 hours
- B.36 hours
- C.24 hours
- D.28 hours
Show answer
Answer: A. 38 hours
. → 2  22 7  21  r  1388 cm2 We know that when any number is divisible by 9 then the sum of the digits of a number should be divisible by 9. → 8 + 7 + 6 + 4 + x + 5 = 30 + x → r = 1388  7 → r = 10.5 22  2  21 Hence, Radius = 10.5 cm
Q8.A tangent is drawn from an external point ‘A’ to a circle of radius 12 cm. If the length of the tangent is 5 cm, then the distance from the centre of the circle to point ‘A’ is: of bc ca ab
- A.17 cm
- B.9 cm
- C.7 cm
- D.13 cm
Show answer
Answer: C. 7 cm
. Highest Profit = 30% in 2016. Now Expenditure = 50 lakh Now Revenue = 50  130  65 lakhs 100 Using options we put → 30 + x = 45 → x = 15 Hence, 15 is the correct Answer.
Q9.The price of a bat and a ball are in the ratio 9 : 5. The price of the bat is Rs.380 more than the price of the ball. Find the price of the ball.
- A.Rs.470
- B.Rs.485
- C.Rs.475
- D.Rs.480
Show answer
Answer: A. Rs.470
. As only 4 can divide both 364 and 724. Hence, 4 is the HCF of 364 and 724.
Q10.The greatest number of five digits which is divisible by 13, 15, 18 and 21 is:
- A.99120
- B.98280
- C.96840
- D.95830
Show answer
Answer: C. 96840
. Given that a + b + c = 0 where a, b, c are non zero. Let a = –1, b = –2 and c = 3 Hence, 65 lakh is the correct Answer. a2  b2  c2  (1)2  (2)2  32
Q11.2 2 2 2 2 2 Total number of boys = 2000A13%C 55%B 32%Total number of boys = 2000A13%C 55%B 32%Study the given pie-chart and answer the question that follows. The pie-chart shows the number of boys studying in play groups of various schools (A, B, C). Total number of boys = 2000 A 13% C 55% B 32% Total number of boys = 2000 A 13% C 55% B 32% What is the average number of boys studying in schools A and C?
- A.740
- B.920
- C.560
- D.680
Show answer
Answer: A. 740
. We have, distance = speed × time Total distance European powers to establish trading outposts and exert influence in the Indian subcontinent. The Portuguese established their presence in India in the and the average speed = According to the question: Total time late 15th century, with Vasco da Gama’s famous voyage in 1498. They initially focused on establishing trading posts 45  x  75  85  3
Q12.In an office, 75 employees can finish a project in 60 days. 6125 1. 165 19 165 6142 165 37 4. 165 After few days, 15 employees left the job and the project was completed in 65 days. After how many days did the 15 The price of a stock increased by 30% in the first year and decreased by 20% in the second year. If an investor bought 100 shares of the stock for `1,000, then what is the final value of the investment after 2 years?
- A.`960
- B.`1,040
- C.`1,400
- D.`1,020
Show answer
Answer: A. `960
. 0.3  x = 0.288
Q13.The LCM of two numbers is 660 and their HCF is 5. If one of the numbers is 55, find the other.
- A.275
- B.12
- C.110
- D.60
Show answer
Answer: D. 60
. x Value of (3.254  3.254  3.254)  (0.746  0.746  0.746) Let Peter invested Rs. x and Rachel invested Rs. 2 . (3.254  3.254)  (0.746  0.746)  (3.254  0.746) PRT   1 r n  (3.254)3  (0.746)3 We have, SI = 100 and CI   P 100   P = (3.254)2  (0.746)2  (3.254)(0.746)     According to the question, Using, a3 – b3 = (a – b) (a2 + b2 + ab) (3.254  0.746) (3.254)2  (0.746)2
Q14.Some medicine in liquid form is prepared in a hemispherical container of diameter 36 cm. When the container is full of medicine, the medicine is transferred to small cylindrical bottles of diameter 6 cm and height 6 cm. How many bottles are required to empty the container?
- A.76
- B.72
- C.70
- D.75
Show answer
Answer: A. 76
. Let the cost price of article = x And profit percentage earned by the third seller = p% 10  69x = 897 2000 2000 According to the question: 120% of x of 125% of (100 + p)% = 165% of x  x  120  125  100  p  165  x  x = 26000 100 100 100 100 So, amount invested by Rachel = Rs. 13000
Q15.Tom can do a piece of work in 7 days, whereas Jay can do the same work in 14 days. How long will they take to finish the work if both work together? employees leave?
- A.50
- B.45
- C.30
- D.40
Show answer
Answer: A. 50
. Percentage increase in price = 10% So, the percentage decrease in consumption 10 100 1 = 100   9 [[IMG:image35.png]] %  120  125  100  p  165 100 100 100 100  100 + p = 110  p = 10%
Q16.Ramesh borrowed `15,000 at a certain rate of simple interest from a bank. He repaid (the principal but not interest) `6,000 after 5 years, and after 5 more years he paid `18,600 and settled his account. Find the rate of simple interest per annum.
- A.12%
- B.10%
- C.8%
- D.6%
Show answer
Answer: A. 12%
.
Q17.Let ABC, PQR be two congruent triangles such that A = P = 90 °. If BC = 17 cm, PR = 8 cm, find AB (in cm).
- A.12
- B.15
- C.14
- D.9
Show answer
Answer: C. 14
. (100 10) 11 11 According to the table: Required percentage = 9  7 13 100 Given that the selling price of table = Rs. 5670 100 So, the cost price = 5670  135  Rs. 4200 112 28  32  46 29 = 106 100  27.36% New selling price when there is profit is 12% = 4200  100 = Rs. 4704
Q18.Total Number of Students = 6700IT21%CSE 22% EEE ECE 12% 10%MECH 27%Total Number of Students = 6700IT21%CSE 22% EEE ECE 12% 10%MECH 27%Study the pie-chart given below, and answer the question that follows. Percentage-wise break up of students in terms of specialisation in BTech Total Number of Students = 6700 IT 21% CSE 22% EEE ECE 12% 10% MECH 27% Total Number of Students = 6700 IT 21% CSE 22% EEE ECE 12% 10% MECH 27% What is the total number of 1. 5 2 3 days 2. 4 2 3 days 3. 7 2 3 days 4. 2 2 days 3 students having specialisation in CSE, ECE and CIVIL? Two trains of lengths 200 m and 250 m are running on parallel rail tracks at speeds of 68 km/h and 50 km/h, respectively. In how much time (in seconds) will they cross each other if they are running in the same direction?
- A.90
- B.85
- C.80
- D.75
Show answer
Answer: C. 80
. Given that the ratio of time taken by cars = 12 : 15 : 10 LCM (12, 15, 10) = 60
Q19.Travelling a distance of 1000 km, a train slowed down due to repairs of the tracks. Its average speed for the trip reduced by 75 km/h and the time of travel increased by 3 hours. The original duration of the travel is:
- A.6 hours
- B.5 hours
- C.5.5 hours
- D.6.5 hours
Show answer
Answer: C. 5.5 hours
. Given that total population of town C = 8000 According to the question: The number of females above the poverty line in state C = 100 – 20 = 80% So, the ratio of speeds of cars = 60 : 60 : 60 12 15 10  5 : 4 : 6 80 = 8000  100 3  8  2400
Q20.337 sin2 A + 3 cos2 A = 4, then find cot A: 3 3
- A.2680
- B.2840 CIVIL8%
- C.2860
- D.2480
Show answer
Answer: C. 2860
. 1 Using, Area of triangle = 2  AB  AC sin A 1 = 2  4  5sin 45 A
Q21.The area of a rectangular field is 480 m2. If the length is 20% 1. 4 cm2 2. 7 cm2 3. 5 cm2 4. 6 cm2 more than the breadth, then the length of the rectangular field If a shopkeeper allows a discount of 10% to his customers and still gains 30%, then the marked price of an article which costs `450 is:
- A.`700
- B.`650
- C.`500
- D.`750
Show answer
Answer: D. `750
. Given that the diameter of a sphere is reduced to its half. Using, Volume of sphere = 4 r3 3 After reducing the diameter, new volume to classify expenditures related to planned development programs and operational expenses, respectively. 4  r 3 22= [[IMG:image33.png]]  [[IMG:image34.png]]  2 2 3   1  4 8  3     r3  = 1  8   (volume of sphere)
Q22.The fourth proportional to 0.3, 0.8 and 0.108 is:
- A.0.144
- B.0.124
- C.0.288
- D.0.482
Show answer
Answer: B. 0.124
. The autobiography of the first Indian President, Dr. Rajendra Prasad, is titled Atmakatha. Atmavrittanta is an autobiography of Manilal Nabhubhai Dwivedi. A Shot at History is the autobiography of Abhinav Bindra, India’s first Olympic gold medalist in shooting. My Country My Life is the autobiography of L.K. Advani, a prominent Indian politician.
Q23.Simplify the given expression. (3.254  3.254  3.254)  (0.746  0.746  0.746) (3.254  3.254)  (0.746  0.746)  (3.254  0.747)
- A.3.156
- B.4.508
- C.2.146
- D.2.508
Show answer
Answer: B. 4.508
. A step towards liberalization typically involves reducing government restrictions and intervention in the economy to promote economic freedom and market-driven growth. The correct policy measure that is a step towards liberalization is option 2: Eliminating licenses for importing a majority of goods.
Q24.is:
- A.30 m
- B.20 m
- C.24 m
- D.27 m
Show answer
Answer: D. 27 m
. Onam is a famous South Indian festival, particularly celebrated in the state of Kerala, which is associated with the legendary King Mahabali. According to the folklore, King Mahabali is believed to visit Kerala during the Onam festival, making it a significant cultural and harvest celebration in the region.
Q25.In a circle centred at O, PQ is a tangent at P. Furthermore, AB is the chord of the circle and is extended to Q. If PQ = 12 cm and QB = 8 cm, then the length of AB is equal to:
- A.20 cm
- B.4 cm
- C.10 cm
- D.8 cm
Show answer
Answer: B. 4 cm
. The Europeans who first entered India with a primary focus on trade were the Portuguese. The French, British, and Dutch also established trading interests in India, but the Portuguese were among the earliest
Q26.The upstream speed of a boat is 8 km/h and the downstream is 15 km/h. What is the speed of the boat in still water and the speed of the stream (in km/h), respectively?
- A.11 and 3
- B.3 and 11
- C.11.5 and 3.5
- D.3.5 and 11.5
Show answer
Answer: A. 11 and 3
. 3888 = 24 × 34 3969 = 72 × 34 So, HCF = 34 = 81
Q27.A number is first decreased by 28% and then increased by 28%. The number so obtained is 784 less than the original number. Find the value of the original number.
- A.1000
- B.15000
- C.10000
- D.1500
Show answer
Answer: A. 1000
. 96 = 25 × 3 108 = 22 × 33 144 = 24 × 32 So, LCM = 25 × 33 = 864
Q28.Hindi 10% Social English 21% 22%Chemistry 12%Mathematics 27%Hindi 10% Social English 21% 22%Chemistry 12%Mathematics 27%Physics8%The following pie chart shows the number of students who failed in different subjects in an examination. Examine the chart and answer the following question. The total number of students who have failed is 350. The number of students failed in mathematics is less than the number of students failed in all other subjects by: Hindi 10% Social English 21% 22% Chemistry 12% Mathematics 27% Hindi 10% Social English 21% 22% Chemistry 12% Mathematics 27% Physics 8%
- A.190
- B.256
- C.95
- D.161
Show answer
Answer: D. 161
. 240 = 24 × 3 × 5 280 = 23 × 7 × 5 560 = 24 × 7 × 5 So, HCF = 23 × 5 = 40
Q29.Simplify the following. 19  5 of 27 15  21  37 In a ΔPQR, P : Q : R = 3 : 4 : 8. The shortest side and the longest side of the triangle, respectively, are:
- A.PQ and PR
- B.QR and PR
- C.PQ and QR
- D.QR and PQ
Show answer
Answer: B. QR and PR
. According to the given table: Required difference = 205 – 198 = 7
Q30.In a triangle ABC, if B = 90°, C = 90° and AC = 4 cm, then the value of BC
- A.2 2 2222cm
- B.4 cm
- C.2 cm
- D.4 cm
Show answer
Answer: D. 4 cm
. According to the given table, There are two years 2002 and 2005 when company Q produces more fabric than company P.

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Frequently Asked Questions

How many SSC CPO (SI Delhi Police & CAPF) Quantitative Aptitude previous year questions are available?

730 Quantitative Aptitude questions from past SSC CPO (SI Delhi Police & CAPF) papers are available on AajExam, split into 73 practice sets. New questions are added as fresh papers are released.

Are the answers and explanations free?

Yes. Every question on this page shows its correct answer and explanation free of charge, and you do not need an account to read them. A free account only adds attempt tracking and performance analytics.

Do SSC CPO (SI Delhi Police & CAPF) repeat questions from previous years?

Exact repeats do occur, but the more reliable pattern is conceptual: the same Quantitative Aptitude sub-topics reappear cycle after cycle with reworded questions. That is why working through past questions raises your score more reliably than reading theory alone.

How should I use these questions in my SSC CPO (SI Delhi Police & CAPF) preparation?

Attempt a set of ten cold, review every wrong and guessed question with its explanation, then drill the weak sub-topic on its topic page before moving on. Revisit the same set after a few days — your second-attempt accuracy is the honest measure of whether the concept stuck.

SSC CPO (SI Delhi Police & CAPF) Quantitative Aptitude practice sets

Each set is a timed 10-question drill drawn from the same question bank.

About SSC CPO (SI Delhi Police & CAPF) Quantitative Aptitude previous year questions

Quantitative Aptitude PYQs asked in SSC CPO (SI Delhi Police & CAPF)

Q1.A truck goes from Haryana to Bangalore with an average speed of 60 km/h. The journey takes 30 hours. It returns from Bangalore to Haryana on the same road with an average speed of 40 km/h. What was the average speed of the truck during the roundtrip?

Q2.In a journey of three unequal laps, a car covers a distance

Q4.If the number 8764x5 is divisible by 9, then find the least possible value of x where x is a two–digit number.

Q5.Find the HCF of 364 and 724.

Q6.If a, b, c are all non-zero and a + b + c = 0, find the value a2  b2  c2 . average speed of the car for entire journey was 50 km/h. What was the speed of the car in the third lap of the journey?

Q7.Three persons P, Q, R run along a circular track at speeds of 3 km/h, 4 km/h, 6 km/h, respectively. If the length of the track is 36 km, then after how much time will they meet again at the starting point?

Q8.A tangent is drawn from an external point ‘A’ to a circle of radius 12 cm. If the length of the tangent is 5 cm, then the distance from the centre of the circle to point ‘A’ is: of bc ca ab

Q9.The price of a bat and a ball are in the ratio 9 : 5. The price of the bat is Rs.380 more than the price of the ball. Find the price of the ball.

Q10.The greatest number of five digits which is divisible by 13, 15, 18 and 21 is:

Q13.The LCM of two numbers is 660 and their HCF is 5. If one of the numbers is 55, find the other.

Q14.Some medicine in liquid form is prepared in a hemispherical container of diameter 36 cm. When the container is full of medicine, the medicine is transferred to small cylindrical bottles of diameter 6 cm and height 6 cm. How many bottles are required to empty the container?

Q15.Tom can do a piece of work in 7 days, whereas Jay can do the same work in 14 days. How long will they take to finish the work if both work together? employees leave?

Q16.Ramesh borrowed `15,000 at a certain rate of simple interest from a bank. He repaid (the principal but not interest) `6,000 after 5 years, and after 5 more years he paid `18,600 and settled his account. Find the rate of simple interest per annum.

Q17.Let ABC, PQR be two congruent triangles such that A = P = 90 °. If BC = 17 cm, PR = 8 cm, find AB (in cm).

Q19.Travelling a distance of 1000 km, a train slowed down due to repairs of the tracks. Its average speed for the trip reduced by 75 km/h and the time of travel increased by 3 hours. The original duration of the travel is:

Q20.337 sin2 A + 3 cos2 A = 4, then find cot A: 3 3

Q22.The fourth proportional to 0.3, 0.8 and 0.108 is:

Q23.Simplify the given expression. (3.254  3.254  3.254)  (0.746  0.746  0.746) (3.254  3.254)  (0.746  0.746)  (3.254  0.747)

Q24.is:

Q25.In a circle centred at O, PQ is a tangent at P. Furthermore, AB is the chord of the circle and is extended to Q. If PQ = 12 cm and QB = 8 cm, then the length of AB is equal to:

Q26.The upstream speed of a boat is 8 km/h and the downstream is 15 km/h. What is the speed of the boat in still water and the speed of the stream (in km/h), respectively?

Q27.A number is first decreased by 28% and then increased by 28%. The number so obtained is 784 less than the original number. Find the value of the original number.

Q29.Simplify the following. 19  5 of 27 15  21  37 In a ΔPQR, P : Q : R = 3 : 4 : 8. The shortest side and the longest side of the triangle, respectively, are:

Q30.In a triangle ABC, if B = 90°, C = 90° and AC = 4 cm, then the value of BC

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