{"id":4392,"date":"2026-09-01T15:58:17","date_gmt":"2026-09-01T10:28:17","guid":{"rendered":"https:\/\/www.catmock.com\/blog\/?p=4392"},"modified":"2026-09-01T15:58:18","modified_gmt":"2026-09-01T10:28:18","slug":"top-20-cat-profit-and-loss-questions-formulas-shortcuts-solved-pyqs","status":"publish","type":"post","link":"https:\/\/www.catmock.com\/blog\/top-20-cat-profit-and-loss-questions-formulas-shortcuts-solved-pyqs\/","title":{"rendered":"TOP 20+ CAT Profit and Loss Questions: Formulas, Shortcuts & Solved PYQs"},"content":{"rendered":"\n

Profit and Loss isn’t a topic you can afford to skip in CAT Quant. Arithmetic makes up close to 35\u201340% of the entire section, and profit and loss sits right at its core alongside percentages and ratios. The concept itself is simple \u2014 Selling Price minus Cost Price \u2014 but CAT dresses it up with successive discounts, false weights, and multi-step transactions designed to slow you down.<\/p>\n\n\n\n

This guide covers the formulas you need, the traps that catch most aspirants, and solved questions you can practice with right away.<\/p>\n\n\n\n

Why This Topic Deserves Your Attention<\/h2>\n\n\n\n

Within Arithmetic, Time-Speed-Distance, Percentages, Profit and Loss, Mixtures, and Ratio carry the maximum weightage. Percentages and Profit & Loss together usually produce 2\u20133 questions per slot, mostly at an easy-to-medium difficulty. That’s a real, learnable chunk of your score \u2014 unlike Geometry, which takes longer to build intuition for.<\/p>\n\n\n\n

Here’s how the topic has actually shown up in recent CAT papers:<\/p>\n\n\n\n

CAT Quant Weightage: 2021 vs 2022 (Average Questions per Slot)<\/h3>\n\n\n\n
Topic<\/th>2021<\/th>2022<\/th><\/tr><\/thead>
Averages, Ratios, Percentage, Mixtures<\/td>4.3<\/td>3.3<\/td><\/tr>
Profit, Loss and Interest<\/td>1.3<\/td>1.3<\/td><\/tr>
Time, Distance and Work<\/td>3<\/td>2.3<\/td><\/tr>
Quadratic Equations<\/td>1.3<\/td>2.3<\/td><\/tr>
Number Systems<\/td>\u2014<\/td>1.7<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n

Profit and Loss rarely disappears from any CAT paper, and it often overlaps with Percentages \u2014 so it’s worth building both together.<\/p>\n\n\n\n

Core Formulas You Need to Know<\/h2>\n\n\n\n
Term<\/th>Meaning<\/th><\/tr><\/thead>
Cost Price (CP)<\/td>Price at which an item is bought<\/td><\/tr>
Selling Price (SP)<\/td>Price at which an item is sold<\/td><\/tr>
Marked Price (MP)<\/td>Listed price before any discount<\/td><\/tr>
Profit<\/td>When SP is greater than CP<\/td><\/tr>
Loss<\/td>When SP is less than CP<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n
Concept<\/th>Formula<\/th><\/tr><\/thead>
Profit %<\/td>[(SP \u2212 CP) \u00f7 CP] \u00d7 100<\/td><\/tr>
Loss %<\/td>[(CP \u2212 SP) \u00f7 CP] \u00d7 100<\/td><\/tr>
SP from Profit %<\/td>SP = CP \u00d7 (1 + P%\/100)<\/td><\/tr>
Successive Profit\/Loss (x%, y%)<\/td>Net% = x + y + xy\/100<\/td><\/tr>
Markup then Discount<\/td>Net% = (1 + m%\/100)(1 \u2212 d%\/100) \u2212 1<\/td><\/tr>
Dishonest Trader (False Weight)<\/td>[(True Weight \u2212 False Weight) \u00f7 False Weight] \u00d7 100<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n

Remember this one: a 40% markup followed by a 25% discount does not cancel out to zero. The discount applies on the marked price, while profit is measured against the cost price. Mixing up these two bases is where most silly mistakes happen.<\/p>\n\n\n\n

Types of Profit and Loss Questions in CAT<\/h2>\n\n\n\n
Question Type<\/th>What It Tests<\/th>Difficulty<\/th><\/tr><\/thead>
Basic CP-SP-Profit%<\/td>Direct formula application<\/td>Easy<\/td><\/tr>
Successive discounts\/markups<\/td>Compounding percentages<\/td>Easy\u2013Medium<\/td><\/tr>
Dishonest shopkeeper (false weight)<\/td>Converting weight tricks into profit%<\/td>Medium<\/td><\/tr>
Mixed selling price<\/td>Weighted average of two transactions<\/td>Medium<\/td><\/tr>
Multi-party resale (A sells to B, B sells to C)<\/td>Tracking CP\/SP across a chain<\/td>Medium\u2013Hard<\/td><\/tr>
Break-even\/contribution problems<\/td>Profit = (Actual sales \u2212 Break-even sales) \u00d7 Contribution per unit<\/td>Hard<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n

Chain-resale problems \u2014 where one person sells to a second, who resells to a third \u2014 show up almost every year in some form. They’re less about formulas and more about carefully tracking whose CP and SP you’re using at each step.<\/p>\n\n\n\n

TITA-based profit and loss questions have also become more common. Since they carry no negative marking, attempt them first if you’re confident with the concept. <\/p>\n\n\n\n

5 Solved Questions with Approach<\/h2>\n\n\n\n

Q1. A vendor bought 6 oranges for \u20b910 and sold them at 4 for \u20b96. Find his loss or profit percentage.<\/strong> <\/p>\n\n\n\n

Take the LCM of 6 and 4 (= 12 oranges) so cost and selling price are compared on the same base. Then apply the standard profit\/loss formula.<\/p>\n\n\n\n

Q2. A shopkeeper sells at cost price but uses a false weight of 900g instead of 1kg. Find his actual profit percentage.<\/strong> <\/p>\n\n\n\n

Always divide by the false weight \u2014 that’s what he actually paid for, not the true weight he claims to sell.<\/p>\n\n\n\n

Q3. A merchant buys two items for \u20b93,000 each, sells one at 20% profit and the other at 20% loss. Find the net result.<\/strong> <\/p>\n\n\n\n

This is the “common gain or loss” trap. Equal-value items sold at equal and opposite percentages always result in a net loss \u2014 never zero. Shortcut: Loss % = (common%\/10)\u00b2.<\/p>\n\n\n\n

Q4. Amar sold a bike to Akbar at a 20% loss. Akbar sold it to Anthony at another 20% loss. Akbar’s loss was \u20b91,200 less than Amar’s. Find Amar’s cost price.<\/strong> <\/p>\n\n\n\n

Let Amar’s CP = x. Find Akbar’s SP (Amar’s post-loss price), then use it as Akbar’s CP. Form an equation using the \u20b91,200 difference and solve.<\/p>\n\n\n\n

Q5. A shopkeeper sells three-fifths of his rice stock at 12% profit and the rest at 7% profit. Find his overall profit percentage<\/strong>.<\/p>\n\n\n\n

Use a weighted average \u2014 multiply each stock fraction by its profit percentage and add \u2014 instead of simply averaging 12% and 7%.<\/p>\n\n\n\n

For more practice at this level, try the CAT PYQ<\/mark><\/a> or attempt a QA Daily Practice test<\/mark><\/a> built around similar arithmetic questions.<\/p>\n\n\n\n

\ud83d\udce5 Want more practice?<\/mark> Download our free CAT Profit and Loss Questions PDF \u2014 20 more solved questions with step-by-step solutions.<\/strong><\/em><\/p>\n\n\n\n

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Download PDF<\/a><\/div>\n<\/div>\n\n\n\n

Common Mistakes to Avoid<\/h2>\n\n\n\n
    \n
  1. Confusing Marked Price with Cost Price<\/strong> \u2014 discounts apply on MP, profit is measured on CP.<\/li>\n\n\n\n
  2. Assuming equal profit and loss percentages cancel out<\/strong> \u2014 they never do; there’s always a net loss.<\/li>\n\n\n\n
  3. Ignoring hidden costs<\/strong> \u2014 add repair or transport charges to CP before computing profit%.<\/li>\n\n\n\n
  4. Dividing by the wrong weight<\/strong> in false-weight problems \u2014 use the false weight, not the true one.<\/li>\n\n\n\n
  5. Losing track of whose CP\/SP you’re using<\/strong> in multi-party resale problems.<\/li>\n<\/ol>\n\n\n\n

    How to Solve Any Profit and Loss Question Faster<\/h2>\n\n\n\n
      \n
    1. Identify the base first<\/strong> \u2014 is the percentage on CP, SP, or MP? This decides your formula.<\/li>\n\n\n\n
    2. Use fractions, not decimals<\/strong> \u2014 20% as 1\/5 is faster to work with mentally.<\/li>\n\n\n\n
    3. Assume convenient values<\/strong> \u2014 if actual CP\/SP isn’t given, assume CP = 100 to simplify.<\/li>\n\n\n\n
    4. Sanity-check the direction<\/strong> \u2014 before finalising, ask if a profit or loss even makes sense here.<\/li>\n<\/ol>\n\n\n\n

      Preparation Timeline<\/h2>\n\n\n\n
      Phase<\/th>Focus<\/th>Practice<\/th><\/tr><\/thead>
      Week 1\u20132<\/td>Formulas, basic CP-SP problems<\/td>15\u201320 questions per sub-topic<\/td><\/tr>
      Week 3\u20134<\/td>Discounts, false weight, mixed SP<\/td>Topic-wise timed sets<\/td><\/tr>
      Week 5\u20136<\/td>Multi-party resale, break-even<\/td>Previous years’ CAT questions<\/td><\/tr>
      Week 7 onward<\/td>Integrate with full mocks<\/td>Full-length CAT mock tests<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n

      Once you’re comfortable with the concepts, move to CAT Full Length Mock Tests<\/mark><\/a> to practice under real exam conditions, or explore the free QA Bhandara<\/mark><\/a> practice sets to drill arithmetic questions at scale. <\/p>\n\n\n\n

      Key Takeaways<\/h2>\n\n\n\n