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SSC CGL Quantitative Aptitude Practice Test Online

SSC CGL Quant isn't about knowing the formula; every aspirant does. It's about doing arithmetic, algebra and geometry clean and fast enough to bank marks in a 50-mark section built to punish hesitation, across CGL, CHSL and CPO.

SSC CGLQuantitative Aptitude
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Reviewed by Anna Nagaraj · Assistant Audit Officer, DG Audit (Railways), Secunderabad · Cleared SSC CGL with All India Rank 442.Fast-track calculation shortcuts, geometry problems, and data-interpretation sets verified for the speed SSC CGL Tier 1 actually demands.

Last reviewed: August 2026

Exam strategy & syllabus overview

Quantitative Aptitude is worth 50 of the 200 marks in SSC CGL Tier 1, spread across 25 questions with +2 for a correct answer and -0.50 for a wrong one. It's the section where 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 the same syllabus repeats across CGL, CHSL and CPO.

The most common mistake is reaching for long-form calculation on a problem that has a shortcut: working out a successive percentage change step by step instead of multiplying the factors directly, or solving a full quadratic when squaring an identity would answer it in one line. With -0.50 per wrong answer, a rushed guess on a lengthy geometry or DI question costs more than skipping it outright. Building genuine calculation speed, not just conceptual understanding, is what turns a passing Tier 1 score into a strong one.

This test matches the SSC CGL Tier 1 Quantitative Aptitude paper exactly: 25 questions, 50 marks, +2 for every correct answer and -0.50 for every wrong one. Speed and accuracy at this Tier 1 pattern build the calculation habits that carry straight into Tier 2's heavier 30-question, +3/-1 Quant module.

⚡ Quick quiz

Test yourself in under a minute: SSC CGL Quantitative Aptitude Practice Test

Seven problems across percentages, time-work, interest and geometry to measure your calculation speed and how quickly you can pick the right formula under pressure.

  1. 1. 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.

  2. 2. 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?

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

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

  5. 5. The centroid of a triangle divides each median in the ratio 2:1 from the vertex. If the length of a median of a triangle is 18 cm, find the distance from the centroid to the midpoint of the opposite side.

  6. 6. In a right triangle, the side opposite to angle theta is 9 cm and the hypotenuse is 15 cm. Find tan(theta).

  7. 7. A table shows the marks scored by 4 students in an exam: Aditi - 78, Bhanu - 65, Chetan - 82, Deepak - 71. What is the difference between the average marks of the top 2 scorers and the average marks of the bottom 2 scorers?

⏱ Cutoff & exam pattern

Target Score: 30-35+ out of 50 in Tier 1 (within 18-20 minutes)

Can you solve a profit-loss, SI/CI, or ratio problem in under 45 seconds without reaching for a formula sheet?

Tier 1 pattern

25 Qs / 50 Marks (+2 / -0.50)

Tier 2 (Module I) pattern

30 Qs / 90 Marks (+3 / -1.00)

Arithmetic Core (%, Profit-Loss, Ratio, Averages)

4-5 Qs / 8-10 Marks

Time, Speed & Work

2-3 Qs / 4-6 Marks

Interest & Mixtures

2-3 Qs / 4-6 Marks

Algebra & Number System

3-4 Qs / 6-8 Marks

Geometry & Mensuration

4-5 Qs / 8-10 Marks

Trigonometry

2-3 Qs / 4-6 Marks

Data Interpretation

3-4 Qs / 6-8 Marks

Time yourself on this set the way you would in the actual exam — accuracy under a clock is the real skill being tested here.

Arithmetic Core: Percentage, Profit & Loss, Ratio & Proportion, Averages

Questions 1-5 cover successive percentage-change calculations, profit-loss-discount chains, a changing-ratio problem, and an averages problem built on consecutive even numbers.

📋 Quick referenceArithmetic Core Quick Reference▶

  • Percentage & profit-loss

    • SP = CP × (1 + profit%/100), or CP × (1 − loss%/100).
    • Successive percentage changes multiply, they don't add (e.g. +20% then −15% = ×1.20×0.85).
  • Ratio word problems: set up the equation with a single variable (e.g. 5x, 8x) before touching the given change.
  • Average of evenly spaced numbers = the middle term; for an even count, it's the average of the two middle terms.

Speed Comes From Relationships, Not Memorized Examples

For Aspirants

  • Identify which relationship a problem is hiding: a rate, a ratio, or a straight percentage.
  • Write the relationship in words first (e.g. 'failing marks + margin = passing marks') before touching numbers.
  • Convert each percentage change to a multiplier before combining the effects.
  • For an even number of equally spaced terms, average the two central terms instead.

  1. 1. 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.

    ▶Reveal answer
    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.

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

    ▶Reveal answer
    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%.

  3. 3. 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%?

    ▶Reveal answer
    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.

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

    ▶Reveal answer
    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.

  5. 5. The average of 7 consecutive even numbers is 40. Find the largest number among them.

    ▶Reveal answer
    46

    For evenly spaced numbers, the average equals the middle term. With 7 terms, the 4th (middle) term is 40, so the numbers are 34, 36, 38, 40, 42, 44, 46, making the largest 46.

Time, Speed & Work: incl. Boats & Streams

Questions 6-7 cover a tank-filling problem with an emptying pipe, and a boats-and-streams downstream-speed problem.

📋 Quick referenceTime, Speed & Work Quick Reference▶
  • Combined work rate = 1/(time A) + 1/(time B); a pipe that empties the tank subtracts its rate.
  • Downstream speed = boat speed + stream speed; upstream speed = boat speed − stream speed.
  • Time = distance / speed, applied after combining rates, not before.

Setting Up the Rate Before Calculating It

For Aspirants

  • Write out exactly what's being compared before calculating: work rates for time-work/pipes, or effective speed for boats and streams.
  • Almost every error in this group comes from combining the wrong two quantities.
  • For boats and streams: downstream speed adds the current, upstream speed subtracts it.

  1. 1. 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?

    ▶Reveal answer
    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.

  2. 2. A boat's speed in still water is 12 km/h, and the speed of the stream is 4 km/h. Find the time taken by the boat to travel 32 km downstream.

    ▶Reveal answer
    2 hours

    Downstream speed = boat speed + stream speed = 12 + 4 = 16 km/h. Time = distance/speed = 32/16 = 2 hours.

  3. 3. Two pipes A and B can fill a tank in 12 hours and 18 hours respectively. If both pipes are opened together, how long will they take to fill the tank?

    ▶Reveal answer
    7.2 hours (36/5 hours)

    Combined rate = 1/12 + 1/18 = 3/36 + 2/36 = 5/36 of the tank per hour. Time to fill = 36/5 = 7.2 hours.

  4. 4. A cyclist covers a distance of 72 km in 4 hours. Find his speed in m/s.

    ▶Reveal answer
    5 m/s

    Speed = 72 km / 4 h = 18 km/h. Converting to m/s: 18 x 5/18 = 5 m/s.

Interest & Mixtures: SI/CI and Alligations

Questions 8-9 cover a compound-interest amount calculation and a mixtures-and-alligations pricing ratio problem.

📋 Quick referenceInterest & Mixtures Quick Reference▶
  • Simple Interest = P×R×T/100; Compound Interest = P×(1+R/100)^T − P.
  • Alligation: ratio of cheaper : dearer quantities = (dearer price − mean price) : (mean price − cheaper price).

One Formula per Concept, Applied Directly

For Aspirants

  • Simple interest grows linearly (same amount each year); compound interest grows on the accumulated total.
  • Always compute the new principal before applying the compound rate again.
  • Place the mean price between the two ingredient prices before calculating the cross-differences.

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

    ▶Reveal answer
    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.

  2. 2. In what ratio must a shopkeeper mix Type A rice costing Rs. 60/kg with Type B rice costing Rs. 45/kg so that the mixture costs Rs. 50/kg?

    ▶Reveal answer
    A:B = 1:2

    Using the alligation rule, ratio of cheaper(B):dearer(A) = (CP of A − mean):(mean − CP of B) = (60−50):(50−45) = 10:5 = 2:1, so B:A = 2:1, meaning A:B = 1:2.

  3. 3. The compound interest on a sum for 2 years at 10% per annum is Rs. 420. Find the simple interest on the same sum for the same period and rate.

    ▶Reveal answer
    Rs. 400

    CI for 2 years at 10% = P x [(1.1)^2 - 1] = P x 0.21 = 420, so P = 2,000. Simple Interest = P x R x T / 100 = 2,000 x 10 x 2 / 100 = Rs. 400.

  4. 4. A mixture of 40 litres contains milk and water in the ratio 3:1. How many litres of water must be added to make the ratio of milk to water 3:2?

    ▶Reveal answer
    10 litres

    The 40-litre mixture has 30 L milk and 10 L water (ratio 3:1). For the ratio to become 3:2, water needed = 30 x (2/3) = 20 L. Additional water required = 20 - 10 = 10 litres.

Algebra & Number System: incl. Surds & Indices

Questions 10-12 cover a linear equation from a sum-and-difference word problem, a laws-of-indices simplification, and a squared-identity algebra problem.

📋 Quick referenceAlgebra & Number System Quick Reference▶
  • Product of two numbers = HCF × LCM.
  • Sum-and-difference word problems: adding the two equations cancels one variable directly.
  • Laws of indices: aᵃ × aᵃ → add exponents; aᵃ ÷ aᵃ → subtract exponents.
  • x + 1/x = k ⇒ x² + 1/x² = k² − 2, so square the given identity instead of solving a quadratic.

Recognizing the Standard Pattern Before Solving

For Aspirants

  • Use the HCF-LCM identity only for two positive integers, then check that the computed partner is integral.
  • For sum-and-difference word problems, write two simple equations and add or subtract them directly.
  • Know the three laws of indices (multiplying, dividing, raising powers) well enough to apply without hesitation.
  • For identities like x + 1/x, square the given identity instead of solving a full quadratic.

  1. 1. The sum of two numbers is 48 and their difference is 12. Find the larger number.

    ▶Reveal answer
    30

    Let the numbers be x and y, with x+y=48 and x-y=12. Adding the two equations gives 2x=60, so x=30 (the larger number) and y=18.

  2. 2. Simplify: (2^5 x 2^3) / 2^6

    ▶Reveal answer
    4

    Using the law of indices a^m x a^n / a^p = a^(m+n-p), the expression simplifies to 2^(5+3-6) = 2^2 = 4.

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

    ▶Reveal answer
    23

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

  4. 4. If one root of the quadratic equation x^2 - 7x + k = 0 is 3, find the value of k and the other root.

    ▶Reveal answer
    k = 12, other root = 4

    Substituting x = 3 gives 9 - 21 + k = 0, so k = 12. Since the sum of the roots of x^2 - 7x + k = 0 is 7 (the negative of the x-coefficient), the other root = 7 - 3 = 4.

Geometry & Mensuration: incl. Triangle Centres, Surface Area & Volume

Questions 13-17 cover circle tangency, a cyclic quadrilateral, rectangle area from perimeter, sphere-to-cones volume recasting, and cylinder surface area.

📋 Quick referenceGeometry & Mensuration Quick Reference▶
  • Centroid divides each median 2:1 from the vertex, always.
  • Two circles touching externally: distance between centres = sum of radii.
  • Cyclic quadrilateral: opposite angles sum to 180°.
  • Recasting one solid into another: total volume stays constant. Equate volumes first, then solve.
  • Cylinder total surface area = 2πr(h + r); don't substitute the volume formula by habit.

Drawing First, Calculating Second

For Aspirants

  • Draw a rough sketch first; labeling angles and sides prevents misreading the question.
  • Identify the named triangle centre before choosing a ratio; centroid, incentre, and circumcentre use different facts.
  • Write both volume expressions with their units before equating them.
  • For surface-area questions, pick the correct formula for that solid instead of defaulting to the volume formula.

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

    ▶Reveal answer
    11 cm

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

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

    ▶Reveal answer
    34

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

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

    ▶Reveal answer
    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.

  4. 4. 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.

    ▶Reveal answer
    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.

  5. 5. Find the total surface area of a cylinder with radius 7 cm and height 10 cm. (Use pi = 22/7)

    ▶Reveal answer
    748 sq cm

    Total surface area of a cylinder = 2*pi*r*(h+r). Substituting r=7, h=10, pi=22/7 gives 2 x 22 x (10+7) = 2 x 22 x 17 = 748 sq cm.

Trigonometry: Ratios, Standard Identities & Heights/Distances

Questions 18-19 cover a standard-identity problem and a heights-and-distances angle-of-elevation problem.

📋 Quick referenceTrigonometry Quick Reference▶
  • tan(angle) = opposite/adjacent; find the missing side with the Pythagorean theorem first if needed.
  • sin²θ + cos²θ = 1 is the fastest route between a known sine and an unknown cosine, or vice versa.
  • Learn the 0°/30°/45°/60°/90° standard values instead of deriving them each time.

Identity First, Then the Diagram

For Aspirants

  • Find the missing side with the Pythagorean theorem before naming the ratio asked for.
  • Standard-identity questions almost always reduce to sin-squared theta + cos-squared theta = 1.
  • For heights and distances, draw the right triangle first, then decide which ratio connects the known values.

  1. 1. If sin(theta) = 3/5, find the value of cos(theta) (theta is acute).

    ▶Reveal answer
    4/5

    Using the identity sin^2(theta) + cos^2(theta) = 1, cos^2(theta) = 1 - 9/25 = 16/25, so cos(theta) = 4/5 (positive since theta is acute).

  2. 2. 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.

    ▶Reveal answer
    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.

  3. 3. Find the value of: 2 sin^2(30 degrees) + cos^2(60 degrees) - tan^2(45 degrees)

    ▶Reveal answer
    -1/4

    sin(30) = 1/2, so 2 x (1/2)^2 = 1/2. cos(60) = 1/2, so (1/2)^2 = 1/4. tan(45) = 1, so (1)^2 = 1. Total = 1/2 + 1/4 - 1 = -1/4.

  4. 4. From the top of a cliff 100 m high, the angles of depression of two boats in the sea, in a straight line with the base of the cliff, are 30 degrees and 45 degrees. Find the distance between the two boats. (Use sqrt(3) = 1.732)

    ▶Reveal answer
    approximately 73.2 m

    The nearer boat (45 degrees) is at distance 100/tan(45) = 100 m. The farther boat (30 degrees) is at distance 100/tan(30) = 100 x sqrt(3), approximately 173.2 m. The distance between the boats = 173.2 - 100 = 73.2 m.

Data Interpretation: Tables, Pie Charts, Bar Graphs & Line Graphs

Questions 20-23 cover a pie-chart-style percentage breakdown, a bar-graph average, a line-graph trend question, and a table-based percentage increase.

📋 Quick referenceData Interpretation Quick Reference▶
  • Table averages: compute each requested subgroup's average separately before comparing or subtracting.
  • Pie chart: find the missing category's percentage as 100% minus the given ones, then convert to a count.
  • Line graph trend questions: compute every consecutive difference once, don't rely on eyeballing the graph.

Reading the Whole Dataset Before Calculating Anything

For Aspirants

  • Read the full table, pie chart, bar graph, or line graph once before answering any part of it.
  • For pie-chart breakdowns, find the missing category's percentage first (100% minus the given ones).
  • For 'which period changed the most' questions, compute every consecutive difference once instead of eyeballing the graph.

  1. 1. 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?

    ▶Reveal answer
    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.

  2. 2. 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.

    ▶Reveal answer
    340 units

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

  3. 3. A line graph shows the monthly rainfall (in mm) of a city: Jan-40, Feb-55, Mar-70, Apr-50, May-85. In which month was the increase in rainfall (compared to the previous month) the highest?

    ▶Reveal answer
    May

    Month-to-month changes are +15 (Feb), +15 (Mar), -20 (Apr), +35 (May). The largest increase over the previous month is +35 mm in May.

  4. 4. 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.

    ▶Reveal answer
    40%

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

  5. 5. A company's sales (in Rs. lakh) over 5 years are: 2019 - 40, 2020 - 55, 2021 - 50, 2022 - 65, 2023 - 70. In which year was the percentage increase in sales over the previous year the highest?

    ▶Reveal answer
    2020

    Percentage change each year: 2020 = (55-40)/40 = 37.5%; 2021 was a decrease; 2022 = (65-50)/50 = 30%; 2023 = (70-65)/65, approximately 7.7%. The highest increase is 37.5% in 2020.

Time-traps & syllabus quirks

  • Percentage, ratio, and profit-loss problems look different on the surface but almost always reduce to the same handful of relationships. Memorizing the underlying relationship, not the specific numbers, saves far more time than memorizing individual example problems.
  • Geometry, mensuration and DI questions are frequently lost to careless unit or arithmetic slips, not to misunderstanding the concept. A quick sanity check before finalizing an answer recovers marks that skill alone wouldn't.
  • Tier 1 is a qualifying screening stage only, so these marks don't carry into your final merit rank. Tier 2 replaces this 6-topic mix with heavier commercial arithmetic, statistics/probability and coordinate geometry, scored at a tougher +3/-1.

Frequently asked questions

How many questions does SSC CGL Quantitative Aptitude have in Tier 1?

25 questions worth 50 marks, with +2 for each correct answer and -0.50 for each wrong answer.

What's a realistic target score for SSC CGL Quant Tier 1?

30-35 out of 50 is a strong target for most aspirants, since Quant is typically slower and more error-prone than Reasoning.

Does my SSC CGL Tier 1 Quant score count toward my final rank?

No. Tier 1 is a qualifying stage only; it filters candidates for Tier 2, but its marks don't add to your final merit score. Tier 2 Quant (Module I) is the exam that actually decides your rank, with a tougher +3/-1 marking scheme and a heavier mix of commercial arithmetic, statistics/probability and coordinate geometry than Tier 1.

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