Profit & Loss and Discount — One Base Rule for Every Question
Syllabus topic: Interest, Profit & Loss, Discount, Partnership
Profit & Loss questions in SSC CGL look varied — dishonest dealers, marked prices, two items sold at the same price — but nearly all of them collapse onto one rule: profit and loss percentages are ALWAYS calculated on the cost price, unless the question explicitly says otherwise.
The vocabulary, fixed once
Cost Price (CP) is what the seller paid; Selling Price (SP) is what the buyer pays; Marked Price (MP) is the tag price before discount. Profit = SP − CP and Loss = CP − SP, and the percentage is that difference divided by CP, multiplied by 100. Discount is the one exception: discount percentage is always calculated on the Marked Price.
Two relations cover most of the section: SP = CP × (100 + profit%)/100 for a gain, and SP = MP × (100 − discount%)/100. When a chain runs CP → MP → SP, apply the relations one step at a time and the answer falls out.
Patterns SSC repeats
When two items are sold at the SAME selling price, one at x% profit and the other at x% loss, the overall result is always a loss of (x/10)² percent — a favourite CGL pattern. When a dealer uses false weights, treat the short weight as an effective price rise: selling 900 g at the price of 1 kg is a gain of (100/900) × 100 ≈ 11.11% before any price markup.
Successive discounts are not additive either: 20% followed by 10% equals a single discount of 20 + 10 − (20×10)/100 = 28%, not 30%. And if the profit percentage is given on SP instead of CP (rare, and always stated), convert before applying the standard formulas.
- Profit% and Loss% are on CP; Discount% is on MP — never mix the bases
- Two items, same SP, x% gain and x% loss → net loss of (x/10)²%
- Successive discounts a% and b% = a + b − ab/100 percent total
A worked check
An article bought for ₹800 is marked 25% above cost and sold at a 10% discount. MP = 800 × 1.25 = ₹1,000. SP = 1,000 × 0.90 = ₹900. Profit = ₹100 on a cost of ₹800, i.e. 12.5%. Notice how the “25% up, 10% down” did not give 15% — the bases differ at every step, which is exactly what the examiner is testing.
Key points to remember
- Profit/Loss % → base is Cost Price. Discount % → base is Marked Price.
- Chain the relations step by step: CP → MP → SP.
- Same-SP gain/loss pattern always ends in a loss of (x/10)²%.
- Successive discounts combine with the −ab/100 correction.
Topic from the official SSC CGL syllabus (Quantitative Aptitude / General Intelligence & Reasoning) as published in NaukriHelp's SSC CGL exam guide. Note written by NaukriHelp; standard mathematics references used for the subject only.