Percentage, profit-loss and discount is the foundation chapter of SSC CGL arithmetic. Half the other chapters — simple and compound interest, ratios, even parts of data interpretation — quietly depend on the same ideas: change expressed as a per cent, computed on the right base. Get this chapter right and you get easier versions of several other chapters for free.
The topic looks huge but it reduces to three prices and one rule. The prices are cost price, marked price and selling price. The rule is: profit and loss are always computed on the cost price, discount is always computed on the marked price. Almost every wrong answer in this chapter comes from applying a percentage to the wrong base.
This chapter covers percentage conversions and successive changes, then CP/SP/MP relations, then the standard profit-loss-discount formulas — each with the exact traps SSC sets around them.
A percentage is just a fraction out of 100. Two things unlock this whole topic: converting per cent to decimals and back without thinking (25% = 0.25 = 1/4), and knowing the common fraction equivalents by heart. When you see '37.5% of 480', converting 37.5% to 3/8 turns a painful multiplication into 3 x 60 = 180.
Formulas:
An increase of x% means multiply the old value by (100 + x)/100; a decrease of x% means multiply by (100 - x)/100. Going backwards — finding the original after a change — means dividing instead of multiplying. This forward-backward fluency is what lets you handle profit-loss and discount questions without setting up equations.
Formulas:
Two successive changes of a% and b% never simply add. Apply them one after another — or use the net formula: net = a + b + (a x b)/100, with + for increase and - for decrease. The classic case: a 10% rise followed by a 10% fall gives 10 - 10 + (10 x -10)/100 = -1%, not zero. The second change acts on the already-changed value.
Formulas:
Three prices, three roles. CP (cost price) is what the seller paid. MP (marked price) is the sticker price. SP (selling price) is what the customer actually pays. Profit and loss are always computed ON THE COST PRICE — 20% profit on CP 500 means SP 600. Discount is always computed ON THE MARKED PRICE — 20% off MP 500 means SP 400. Getting the base right (CP for profit, MP for discount) is the whole chapter.
Formulas:
Single-equivalent discount uses the same successive-change logic: two discounts d1 and d2 equal one discount of (d1 + d2 - d1 x d2/100)%. Notice the minus — two successive discounts are always worth LESS than their sum (20% + 10% = 28%, not 30%). And a frequent SSC trick: if a shopkeeper marks up by m% and then gives d% discount, profit% = m - d - m x d/100.
Formulas:
Answer: 36
Answer: 1% loss
Answer: 15%
Answer: Rs. 800; 25% profit
Answer: Rs. 1050
Answer: 80
25% = 1/4; 320/4 = 80.
Answer: Rs. 600
SP = 500 x (100 + 20)/100 = 500 x 1.2 = Rs. 600.
Answer: Rs. 1700
SP = 2000 x (100 - 15)/100 = 2000 x 0.85 = Rs. 1700.
Answer: 4% loss
20 + (-20) + (20 x -20)/100 = -4%. A 4% net loss.
Answer: Rs. 600
CP = 750 x 100/125 = 750 x 0.8 = Rs. 600.
Profit and loss are always computed on the cost price. The only exception is when the question explicitly says otherwise ('profit on selling price') — rare, and it will be stated in words.
Two successive changes of 10% do NOT make 20% — the second change acts on the already-changed value. Use the net formula: a + b + (a x b)/100 with correct signs. 10% up then 10% down = -1%.
Check which price the per cent is applied to. In a profit question, the base is CP; in a discount question, the base is MP. Most wrong answers in this chapter come from applying the percentage to the wrong base.
It changes the profit base. Selling above CP gives profit; selling below CP gives loss. If the question gives profit on SP or profit on MP, convert carefully — and confirm with the options before moving on.