About this SSC CGL Quantitative Aptitude practice test

Quantitative Aptitude is the section where SSC CGL candidates lose the most time relative to marks gained, because the math itself — Arithmetic, Algebra, Geometry, Mensuration, Trigonometry and Data Interpretation — is rarely hard, just numerous. Arithmetic alone covers Percentage, Ratio & Proportion, Profit/Loss, Simple/Compound Interest, Time & Work and Speed/Distance/Time, and building genuine calculation speed here — not just conceptual understanding — is what separates a good Tier 1 score from a great one across CGL, CHSL and CPO.

SSC CGL Quantitative Aptitude Practice Test sample questions

These starter questions help you launch a quantitative aptitude mock test quickly. Swap them with your own worksheet, notebook, or textbook questions any time.

1. 1. The HCF of two numbers is 12 and their LCM is 504. If one of the numbers is 72, find the other number.

2. 2. Find the smallest number which, when divided by 8, 12, and 15, leaves a remainder of 5 in each case.

3. 3. How many numbers between 1 and 500 are divisible by both 7 and 11?

4. 4. In an examination, a candidate needs 45% of the total marks to pass. A student scored 189 marks and failed by 36 marks. Find the maximum marks of the examination.

5. 5. The population of a town increases by 20% in the first year and decreases by 15% in the second year. If the population after two years is 30,600, find the initial population.

6. 6. A shopkeeper marks his goods 40% above the cost price and allows a discount of 15% on the marked price. Find his profit percentage.

7. 7. By selling an article for Rs. 665, a trader incurs a loss of 5%. At what price should he sell the article to gain a profit of 8%?

8. 8. A dealer allows a discount of 10% on the marked price of an article and still earns a profit of 26%. If the cost price of the article is Rs. 450, find its marked price.

9. 9. A sum of Rs. 12,000 amounts to Rs. 15,600 in 3 years at simple interest. Find the rate of interest per annum.

10. 10. Find the compound interest on Rs. 8,000 for 2 years at 15% per annum, compounded annually.

11. 11. The ratio of two numbers is 5:8. If 10 is added to each number, the ratio becomes 7:10. Find the two numbers.

12. 12. A, B and C invest Rs. 15,000, Rs. 20,000 and Rs. 25,000 respectively in a business. If the total profit at the end of the year is Rs. 48,000, find B's share of the profit.

13. 13. A and B start a business with capitals of Rs. 20,000 and Rs. 15,000 respectively. A withdraws his capital after 6 months, while B continues investing for the full year. If the total profit at the end of the year is Rs. 25,000, find A's share of the profit.

14. 14. A can complete a piece of work in 18 days and B can complete the same work in 24 days. They work together for 6 days, after which A leaves. In how many more days will B alone finish the remaining work?

15. 15. Pipe A can fill a tank in 20 hours and pipe B can fill it in 30 hours, while pipe C can empty the full tank in 15 hours. If all three pipes are opened together, in how many hours will the tank be filled?

16. 16. A train 180 metres long crosses a platform 270 metres long in 30 seconds. Find the speed of the train in km/h.

17. 17. A man travels a certain distance by car at 60 km/h and returns the same distance at 40 km/h. Find his average speed for the entire journey.

18. 18. Two stations, A and B, are 410 km apart. A train starts from station A at 7:00 am at a speed of 50 km/h towards station B. Another train starts from station B at 8:00 am at a speed of 70 km/h towards station A. At what time will the two trains meet?

19. 19. If x + 1/x = 5, find the value of x^2 + 1/x^2.

20. 20. The sum of a number and its reciprocal is 26/5. Find the number.

21. 21. In a triangle, the angles are in the ratio 2:3:4. Find the measure of the largest angle.

22. 22. Two circles of radii 8 cm and 3 cm touch each other externally. Find the distance between their centres.

23. 23. ABCD is a cyclic quadrilateral in which angle A = (2x + 15) degrees and angle C = (3x - 5) degrees. Find the value of x.

24. 24. The length of a rectangular field is 25% more than its breadth. If the perimeter of the field is 180 m, find its area.

25. 25. A solid metallic sphere of radius 6 cm is melted and recast into small cones, each of radius 3 cm and height 4 cm. Find the number of cones formed.

26. 26. The angle of elevation of the top of a tower from a point on the ground 50 m away from its base is 30 degrees. Find the height of the tower.

27. 27. From the top of a building 60 m high, the angle of depression of a car parked on the ground is 30 degrees. Find the distance of the car from the base of the building.

28. 28. A table shows the number of books sold by a store over four months: January - 240, February - 300, March - 200, April - 280. Find the percentage increase in sales from March to April.

29. 29. A survey of 600 students shows their preferred subjects as follows: Mathematics - 33%, Science - 25%, English - 20%, and the remaining students prefer Social Studies. How many students prefer Social Studies?

30. 30. A bar graph shows the number of units produced by a factory over four weeks: Week 1 - 320, Week 2 - 410, Week 3 - 250, Week 4 - 380. Find the average weekly production.

Answer key & quick explanations

Short answers for the sample questions above. Use this to self-check before generating a fresh AI-built mock test.

1. 1. HCF-LCM: find the other number

   84

   Since the product of two numbers equals the product of their HCF and LCM, the other number = (12 x 504)/72 = 6048/72 = 84.

2. 2. Smallest number leaving remainder 5

   125

   LCM of 8, 12 and 15 is 120. A number that leaves remainder 5 when divided by each must be 120k + 5; the smallest such number is 120 + 5 = 125.

3. 3. Count of numbers divisible by 7 and 11

   6

   A number divisible by both 7 and 11 must be divisible by their LCM, 77. Between 1 and 500, the multiples of 77 are 77, 154, 231, 308, 385 and 462, giving 6 numbers.

4. 4. Maximum marks from pass/fail data

   500

   Passing marks = 189 + 36 = 225. Since 225 represents 45% of the maximum marks, the maximum marks = 225/0.45 = 500.

5. 5. Initial population after two % changes

   30,000

   A 20% increase followed by a 15% decrease multiplies the population by 1.20 x 0.85 = 1.02. So initial population = 30,600/1.02 = 30,000.

6. 6. Profit % after markup and discount

   19%

   Taking CP = 100, the marked price = 140. A 15% discount on 140 is 21, giving SP = 119. Profit = 119 - 100 = 19, so profit percentage = 19%.

7. 7. New selling price for 8% gain

   Rs. 756

   Since Rs. 665 represents a 5% loss, CP = 665/0.95 = Rs. 700. To gain 8%, the new SP = 700 x 1.08 = Rs. 756.

8. 8. Marked price from profit and discount

   Rs. 630

   SP = CP x 1.26 = 450 x 1.26 = Rs. 567. Since this SP is 90% of the marked price (10% discount), MP = 567/0.90 = Rs. 630.

9. 9. Rate of simple interest

   10% per annum

   SI = 15,600 - 12,000 = Rs. 3,600. Rate = (SI x 100)/(P x T) = (3600 x 100)/(12000 x 3) = 10% per annum.

10. 10. Compound interest for 2 years at 15%

    Rs. 2,580

    Amount = 8000 x (1.15)^2 = 8000 x 1.3225 = Rs. 10,580. Compound interest = 10,580 - 8,000 = Rs. 2,580.

11. 11. Two numbers from a changing ratio

    25 and 40

    Let the numbers be 5x and 8x. Then (5x+10)/(8x+10) = 7/10, which gives 50x+100 = 56x+70, so x = 5. The numbers are 25 and 40.

12. 12. B's share in partnership profit

    Rs. 16,000

    The investment ratio 15000:20000:25000 simplifies to 3:4:5, totalling 12 parts. B's share = (4/12) x 48,000 = Rs. 16,000.

13. 13. A's share with unequal investment periods

    Rs. 10,000

    A's capital-months = 20,000 x 6 = 1,20,000 and B's = 15,000 x 12 = 1,80,000, giving a ratio of 2:3. A's share = (2/5) x 25,000 = Rs. 10,000.

14. 14. Remaining work time for B alone

    10 days

    Combined 1-day work of A and B = 1/18 + 1/24 = 7/72. In 6 days they complete 6 x 7/72 = 7/12 of the work, leaving 5/12. At B's rate of 1/24 per day, B needs (5/12) / (1/24) = 10 days.

15. 15. Time to fill tank with an emptying pipe

    60 hours

    Combined rate = 1/20 + 1/30 - 1/15 = 3/60 + 2/60 - 4/60 = 1/60 of the tank per hour. So the tank fills in 60 hours.

16. 16. Speed of train crossing a platform

    54 km/h

    The train covers its own length plus the platform length: 180 + 270 = 450 m in 30 seconds, giving a speed of 15 m/s, which equals 15 x 18/5 = 54 km/h.

17. 17. Average speed for a round trip

    48 km/h

    For equal distances covered at two different speeds, average speed = (2 x 60 x 40)/(60+40) = 4800/100 = 48 km/h.

18. 18. Meeting time of two trains

    11:00 am

    By 8:00 am the first train has already covered 50 km, leaving 410 - 50 = 360 km between the trains. Closing at a combined speed of 50+70 = 120 km/h, they meet after 360/120 = 3 hours, i.e., at 11:00 am.

19. 19. Value of x^2 + 1/x^2

    23

    Squaring x + 1/x = 5 gives x^2 + 1/x^2 + 2 = 25, so x^2 + 1/x^2 = 25 - 2 = 23.

20. 20. Number whose sum with its reciprocal is 26/5

    5 or 1/5

    Writing x + 1/x = 26/5 gives 5x^2 - 26x + 5 = 0. Factoring or using the quadratic formula gives x = 5 or x = 1/5, both of which satisfy the original equation.

21. 21. Largest angle in a 2:3:4 triangle

    80 degrees

    The three angles total 9 equal parts summing to 180 degrees, so each part is 20 degrees. The largest angle, 4 parts, equals 4 x 20 = 80 degrees.

22. 22. Distance between centres of externally touching circles

    11 cm

    When two circles touch externally, the distance between their centres equals the sum of their radii: 8 + 3 = 11 cm.

23. 23. Value of x in a cyclic quadrilateral

    34

    Opposite angles of a cyclic quadrilateral sum to 180 degrees, so (2x+15) + (3x-5) = 180, giving 5x + 10 = 180 and x = 34.

24. 24. Area of a rectangular field from perimeter

    2000 sq. m

    Let breadth = b, so length = 1.25b. Perimeter = 2(b + 1.25b) = 4.5b = 180, giving b = 40 m and length = 50 m. Area = 40 x 50 = 2000 sq. m.

25. 25. Number of cones recast from a sphere

    24

    Volume of the sphere = (4/3) x pi x 6^3 = 288 x pi cubic cm, and volume of one cone = (1/3) x pi x 3^2 x 4 = 12 x pi cubic cm. Number of cones = 288 x pi / 12 x pi = 24.

26. 26. Height of a tower from angle of elevation

    50/sqrt(3) m, approximately 28.9 m

    Using tan(30 degrees) = height/50, height = 50 x tan30 = 50/sqrt(3) = (50 x sqrt(3))/3, which is approximately 28.9 m.

27. 27. Distance of a car from angle of depression

    60 x sqrt(3) m, approximately 103.9 m

    The angle of depression equals the angle of elevation from the car, so tan(30 degrees) = 60/distance, giving distance = 60/tan30 = 60 x sqrt(3), approximately 103.9 m.

28. 28. Percentage increase in sales, March to April

    40%

    Sales rose from 200 in March to 280 in April, an increase of 80. Percentage increase = (80/200) x 100 = 40%.

29. 29. Number of students preferring Social Studies

    132

    Mathematics, Science and English together account for 33+25+20 = 78% of students, leaving 22% for Social Studies. Number of students = 22% of 600 = 132.

30. 30. Average weekly production

    340 units

    Total production over four weeks = 320+410+250+380 = 1,360 units. Average weekly production = 1,360/4 = 340 units.

Curriculum Mapping & Learning Guide

Use this breakdown to identify which skills each question tests and guide post-test review.

SSC CGL Quantitative Aptitude units covered

1. Chapter 1: Number System (HCF, LCM, Divisibility)
2. Chapter 2: Percentage and Its Applications
3. Chapter 3: Profit, Loss and Discount
4. Chapter 4: Simple and Compound Interest
5. Chapter 5: Ratio, Proportion and Partnership
6. Chapter 6: Time, Work and Pipes
7. Chapter 7: Speed, Distance and Time
8. Chapter 8: Algebra (Linear and Quadratic Equations)
9. Chapter 9: Geometry (Triangles, Circles, Quadrilaterals)
10. Chapter 10: Mensuration (Area, Volume — 2D and 3D)
11. Chapter 11: Trigonometry (Ratios, Heights & Distances)
12. Chapter 12: Data Interpretation (Tables, Bar Graphs, Pie Charts)

Quantitative Aptitude practice tests for other exams and classes

Continue the same quantitative aptitude thread across nearby exams and school classes for year-on-year revision.