Profit, Loss & Discount: Formulas, Shortcuts & Tricks for SSC, Bank and Railway Exams

The three prices

Profit = SP - CP and loss = CP - SP. Profit % = profit/CP × 100. Example: CP Rs 450, SP Rs 540. Profit = 90, profit % = 90/450 × 100 = 20%.

Core formulas

Discounts

• Discount % = discount/MP × 100, never on CP.
• Successive discounts: 30% then 20% equals a single discount of 30 + 20 - 600/100 = 44% (100 becomes 70, then 56).
• Mark-up and discount together: marked 50% above CP, then 20% off gives 50 - 20 - 10 = 20% profit (1.5 × 0.8 = 1.2).
• To find MP when CP, discount and profit are known: MP/CP = (100 + P%)/(100 - D%).

Dishonest dealers (false weights)

A trader who gives less than he claims gains on the weight. Gain % = (true - false)/false × 100. Using 950 g for a kilogram gives 50/950 × 100 = 5 5/19 %. If he also marks up, multiply the factors: selling at 10% above cost with an 800 g weight gives 1.1/0.8 = 1.375, a 37.5% gain.

Articles for articles

• If the CP of x articles equals the SP of y articles, profit % = (x - y)/y × 100. CP of 18 = SP of 15 gives 3/15 = 20% profit (a loss if y > x).
• Bought a items for Rs b and sold c items for Rs d: compare price per item. Bought 8 for Rs 10 (1.25 each), sold 10 for Rs 15 (1.50 each): profit = 0.25/1.25 = 20%.

Same selling price, equal gain and loss

Two items each sold for the same price, one at x% profit and the other at x% loss, always give a net LOSS of x²/100 %. Example: two phones each sold for Rs 12,000, one at 20% gain and one at 20% loss. CPs are 10,000 and 15,000, total 25,000; total SP 24,000, so a loss of Rs 1,000 = 4% (= 20²/100).

Offers and special cases

• Buy 4 get 1 free: you pay for 4 and receive 5, so the discount is 1/5 = 20%.
• Profit at SP1 equals loss at SP2: CP is midway, CP = (SP1 + SP2)/2. Profit at Rs 780 equals loss at Rs 620, so CP = Rs 700.
• Two successive profits a% and b% on the same item (as it changes hands) combine like successive percentages: a + b + ab/100.