Everything in this chapter rests on one fact: profit % and loss % are always measured on the cost price (CP), never on the selling price.
The four core moves
• CP → SP: multiply. SP = CP × 100100+profit%. A 20% profit means ×56, a 25% profit means ×45.
• SP → CP: divide by the same factor. CP = SP × 100±%100. Never just subtract the % from SP.
• Profit% = CPSP−CP×100; Loss% = CPCP−SP×100.
The fastest route is to turn each % into a clean fraction multiplier and cancel.
💵Profit / Loss Calculator% is always on CP
cost price
selling price
= |600−500| ÷ 500 × 100 = 20% profit
CP ₹400 at 25% profit: SP = 400 × 45 = ₹.
📝Practice Questions
Q1CP ₹400, sold at 25% profit. SP is:
Q2Sold for ₹450 at 25% loss. CP is:
Q3CP ₹500, SP ₹575. Profit% is:
📚
Real exam questions — CP, SP, Profit & Loss
1 question types · 4 solved examples from real SSC papers
CP is the base — every profit% and loss% sits on it. Turn each % into a clean multiplier and these fly.
How to solve this type
Cost Price (CP) is the base — every profit % or loss % is taken on CP, never on SP. To go from CP to SP, multiply: SP = CP×100100+profit% (use 100−loss% for a loss). To come back from SP to CP, divide by the same factor: CP = SP×100±%100. To find the rate from two prices, use Profit% = CPSP−CP×100 (and Loss% = CPCP−SP×100). Read carefully whether the % sits on a profit or a loss, and never apply it to the selling price.
A shopkeeper buys an article for ₹2,500 and sells it at 20% profit. Find the selling price (in ₹).
A3,100B2,950C3,000D2,800
An article is sold for ₹6,500 at 4% profit. What is the cost price (in ₹)?
A6,150B6,000C6,250D6,300
Mihir buys a book for ₹625 and sells it for ₹550. Find his loss percentage.
A12%B15%C14%D10%
By selling a table for ₹1,596, Aarav loses 24%. What is the CP (in ₹)?
