Basic Mathematics MCQs with Answers and Solutions
Quantitative ability is tested in nearly every recruitment and admission test in Pakistan, from PPSC, FPSC, KPPSC, SPSC and BPSC papers to NTS, OTS, ETEA, GAT, armed forces initial tests and CSS screening. These basic mathematics MCQs with answers are arranged by topic so you can practise one area at a time: number system and arithmetic, algebra, geometry and mensuration, percentage, profit and loss, average, mean, median and mode, speed, time and distance, probability and permutations, ratio, proportion and ages, time and work, simple and compound interest, number series, clocks and calendars and trigonometry. Every answer has been worked out and checked, and each MCQ appears on only one topic page.
Take a scored quiz instead →Maths Formulas Every Test Candidate Should Know
Most mathematics MCQs in competitive tests can be solved in under a minute if you know the right formula. The tables below collect the shortcuts that come up again and again. Revise them first, then open the topic pages above and practise until the method becomes automatic.
Arithmetic and commercial maths
| Topic | Formula or shortcut |
|---|---|
| Profit or loss % | (Profit or Loss ÷ Cost Price) × 100 |
| Selling price | CP × (100 + Gain%) ÷ 100, or CP × (100 − Loss%) ÷ 100 |
| Successive changes of a% and b% | Net change = a + b + ab/100 (use minus signs for decreases) |
| Simple interest | SI = P × R × T ÷ 100 |
| Compound interest | Amount = P × (1 + R/100)T; CI = Amount − P |
| SI and CI difference for 2 years | P × (R/100)² |
| Product of two numbers | HCF × LCM |
| Average | Sum of observations ÷ number of observations |
Speed, work and time
| Topic | Formula or shortcut |
|---|---|
| Speed | Distance ÷ Time; km/h × 5/18 = m/s |
| Train crossing a pole / platform | Time = train length ÷ speed / (train + platform length) ÷ speed |
| Boats and streams | Downstream = boat + stream; upstream = boat − stream |
| Average speed for equal distances | 2xy ÷ (x + y) |
| Two workers together | Time = ab ÷ (a + b) days |
| Men and days | M₁ × D₁ = M₂ × D₂ |
| Pipe filling with a leak | Net rate = 1/fill time − 1/empty time |
Algebra, geometry and trigonometry
| Topic | Formula |
|---|---|
| Algebraic identities | (a + b)² = a² + 2ab + b²; a² − b² = (a + b)(a − b); a³ + b³ = (a + b)(a² − ab + b²) |
| Quadratic roots | x = [−b ± √(b² − 4ac)] ÷ 2a; sum of roots = −b/a, product = c/a |
| nth term of an AP | a + (n − 1)d; sum = n/2 × [2a + (n − 1)d] |
| Interior angles of a polygon | (n − 2) × 180°; exterior angles always total 360° |
| Circle | Area = πr²; circumference = 2πr |
| Cylinder, cone, sphere | Volume = πr²h, ⅓πr²h and ⁴⁄₃πr³ |
| Pythagoras theorem | Hypotenuse² = base² + perpendicular² |
| Trigonometric values | sin 30° = cos 60° = ½; tan 45° = 1; sin²θ + cos²θ = 1 |
Frequently Asked Questions
Which maths topics are asked most in PPSC, FPSC and NTS tests?
Percentage, profit and loss, average, ratio and proportion, simple and compound interest, time and work, and speed, time and distance make up most of the arithmetic section. Basic algebra, geometry formulas and number series follow. Questions are usually short and are meant to be solved without a calculator.
How can I solve maths MCQs faster in competitive exams?
Learn the formulas and shortcuts above, practise one topic at a time, and check the options before calculating, because the answer can often be found by elimination or by substituting an option back into the question. Leave long questions for the end and come back to them if time allows.
What is the difference between simple and compound interest?
Simple interest is calculated only on the original principal, so it is the same every year. Compound interest is calculated on the principal plus the interest already earned, so it grows each period. On Rs. 1,000 at 10% for 2 years, simple interest is Rs. 200 while compound interest is Rs. 210.
How do you find the time taken when two people work together?
Add their one-day work. If A finishes a job in 10 days and B in 15 days, together they do 1/10 + 1/15 = 1/6 of the job per day, so they finish it in 6 days. The shortcut is ab ÷ (a + b).
Is a calculator allowed in NTS and PPSC tests?
Calculators are generally not allowed in these written tests, so questions are designed to be solved mentally or with simple working on rough paper. Check the instructions on your admit card for the specific test.