All 48 Algebra questions the Punjab PSC asked between 2015 and 2026, each with a worked answer and the exam it came from. First 10 free to read.
5 of these 48 were set in more than one exam — the Commission reuses this topic, which is the argument for working through it rather than skimming it.
Free to read, with the worked answer and the exam each one came from. The book prints this topic in the order the Commission favours, so these are the ones to know first.
Let n friends plan the picnic. Each was to pay 96/n. Four dropped out, so each of the n − 4 paid ₹4 more. > 96/(n − 4) − 96/n = 4 > 96 × 4 = 4n(n − 4) → n² − 4n − 96 = 0 → (n − 12)(n + 8) = 0 → n = 12 So 12 planned and 12 − 4 = 8 attended. Each paid ₹12 instead of ₹8. The question asks how many attended, not how many planned.
Let a pair of jeans cost j and a T-shirt cost t. > 2j + 4t = 1600 and j + 6t = 1600 > Double the second: 2j + 12t = 3200; subtract the first: 8t = 1600 → t = 200, j = 400 > 3j + 5t = 1200 + 1000 = 2200 So 3 jeans and 5 T-shirts cost ₹ 2,200.
Let the fare to B be x and to C be y. So 2x + 3y = 77 and 3x + 2y = 73. > adding: 5x + 5y = 150 → x + y = 30 > subtracting: x − y = 73 − 77 = −4 > x = 13, y = 17 The fares are ₹ 13 to B and ₹ 17 to C. A quick check confirms it: 2(13) + 3(17) = 77 and 3(13) + 2(17) = 73.
Let C hold c cards. A gives 8 cards to B, and B then equals C, so B = c − 8. A is then 3 short of C, so A − 8 = c − 3, that is A = c + 5. If A takes 6 cards from C, A has twice D's cards, so A + 6 = 2D and D = (c + 11)/2. > B + D = 50 → (c − 8) + (c + 11)/2 = 50 > 2c − 16 + c + 11 = 100 → 3c = 105 → c = 35 > A = 35 + 5 = 40, B = 27, D = 23 So A holds 40 cards. The numbers 27 and 23 are B's and D's counts, put there as distractors.
Let there be b benches. With 4 per bench and 3 benches empty, the students number 4(b − 3). With 3 per bench and 3 standing, they number 3b + 3. > 4(b − 3) = 3b + 3 → 4b − 12 = 3b + 3 → b = 15 > Students = 3 × 15 + 3 = 48 Check: 4 × 12 = 48.
Let P and Q be the quantities of milk in the two vessels. > P − 20 = Q + 20 → P = Q + 40 > P + 40 = 2(Q − 40) → Q + 80 = 2Q − 80 → Q = 160 > P = 160 + 40 = 200 Check: pour 20 litres from P to Q and each has 180 litres. Pour 40 litres from Q to P and they hold 240 and 120, which is double.
Call the fraction f; it is 7/15 more than twice its reciprocal. > f = 2/f + 7/15 > 15f² − 7f − 30 = 0 > f = (7 + 43)/30 = 50/30 The fraction is 5/3.
Use the identity a³ − b³ = (a − b)³ + 3ab(a − b). > 91 = 1³ + 3ab × 1 > 3ab = 90 So ab = 30.
Let the fixed amount be F and the royalty per copy be r. > F + 500r = 750 and F + 1350r = 1175 > 850r = 425 → r = ₹0.50, F = ₹500 > Receipt at 10,000 copies = 500 + 0.5 × 10,000 = ₹5,500 > Additional amount = 5,500 − 1,175 = ₹4,325. ₹5,500 is the total, not the additional amount.
Let the number of cows be c and hens be h. Each animal has one head. A cow has 4 legs and a hen has 2. > c + h = 45 > 4c + 2h = 130 → 2c + h = 65 > subtracting: c = 20, h = 25 There are 20 cows. That value is not in the options, so the answer is None of these.
You have read the ten the Commission asks most. The rest of this topic — and all 4,239 questions across the book, each with a worked solution — come with either edition.
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536 pages, delivered. Five full papers and five OMR sheets at the back. Online access is included free, from the moment you pay.
See the printed book →The Commission set 48 Algebra questions across 50 papers between 2015–2026. That is the whole set, not a sample — every one of them is in the book, and the 10 most-asked are on this page free.
Yes. 5 of these 48 were set in more than one exam, which is why they are worth working rather than reading. Each question here carries a badge showing how many sittings asked it.
Here. Every question on this page is a solved MCQ: the four options as printed, the correct answer, and a worked explanation in plain English — not just a letter. The rest of the 48 are in the book, in the same form.
Switch to Attempt mode at the top of the questions. You get one question at a time and it is marked the moment you pick an option, with the reason underneath — the same way the exam feels, on your phone.
The questions are on screen rather than in a downloadable file, so they stay current and correct. The printed book has all 48 of these plus the rest of the Reasoning & Aptitude section, and every buyer gets the whole thing online as well.
The exams behind these questions, most first. A paper here is a sitting: a question set in two papers of the same sitting counts once.
| Exam | Year | Questions |
|---|---|---|
| Extra Assistant Conservator of Forests in the the Department of Forest and Wild | 2019 | 8 |
| Assistant Mechanical Engineer | 2018 | 4 |
| Planning Officer (Group A) | 2024 | 3 |
| Naib Tehsildar | 2023 | 3 |
| Punjab Civil Services (Prelims) — CSAT | 2025 | 2 |
| Superintendent Home (Group-B) | 2024 | 2 |
| District Social Security Officer (Group-B) | 2024 | 2 |
| Building Inspector (Technical)(Group B)in the Department of Local Government (Mu… | 2022 | 2 |
| Analysts | 2022 | 2 |
| Accountants | 2022 | 2 |
| Building Inspector (Technical)(Group B) | 2022 | 2 |
| Block Primary Education Officer | 2020 | 2 |