Profit and Loss Questions for AGNIVEER ARMY

Basic Definitions

Cost Price (CP) is the price at which an item is bought. Selling Price (SP) is the price at which it is sold. If SP is more than CP, there is Profit. If SP is less than CP, there is Loss. Overhead charges like transport or repair are always added to CP before calculating profit or loss.

• Profit = SP - CP (when SP > CP)
• Loss = CP - SP (when CP > SP)
• Profit % and Loss % are always calculated on CP, not SP
• If extra expenses are given (like repair cost), add them to CP first
• Marked Price (MP) is the listed price before any discount

Discount and Marked Price

Marked Price (MP) is what the shopkeeper writes on the tag. Discount is the reduction given on MP. The actual SP after discount is MP minus Discount. Profit or loss is still calculated using CP. Agniveer papers often combine discount with profit percent in one question — this is the most common trap.

• Discount = MP - SP
• Discount% = (Discount / MP) x 100
• SP = MP x (100 - Discount%) / 100
• To find CP when MP, discount%, and profit% are all given: first find SP from MP, then find CP from SP
• Discount is on MP, Profit/Loss is on CP — never mix these two bases

Dishonest Dealer and False Weight

A common Agniveer question type: a dealer claims to sell at cost price but uses a false weight (less than actual). This means the buyer gets less quantity but pays for more. The dealer profits because he gives less. The formula for profit percent using false weights is a direct formula — memorize it and apply directly.

• Dealer uses false weight means he gives less grams than he claims
• If true weight is 1000g but he gives only 900g, he profits on the 100g kept
• Profit% = (True weight - False weight) / False weight x 100
• This profit is made even when selling at cost price
• Agniveer papers give this in terms of grams — just plug into the formula

Two Articles Sold at Same SP - One Profit One Loss

A classic trap question: two items sold at the same SP, one at x% profit and one at x% loss. Most students think it breaks even. It never does — there is always a net loss. The formula gives a direct answer. This appears frequently in Agniveer as a one-liner tricky question.

• When two articles sold at same price, one at x% profit and x% loss, the net result is always a LOSS
• Loss% = (Common percent)^2 / 100
• This formula only works when profit% and loss% are equal
• Overall loss is on total CP — you never break even in this case
• Always remember: same SP with same percent = net loss

• Calculating profit% or loss% on SP instead of CP — always use CP as the base for these percentages
• Forgetting to add repair or overhead cost to CP before calculating profit — this changes the entire answer
• In discount problems, applying discount on CP instead of on Marked Price — discount is always on MP
• In the false weight problem, dividing by True weight instead of False weight — formula uses False weight in denominator
• Assuming that selling at same SP with equal profit% and loss% gives zero overall result — it always gives a net loss

• PSCP rule: Profit and loss percent are always on CP. Say it loud: P-S-C-P (Percent Stays on Cost Price)
• For two-item equal SP trick remember: Same Price Same Percent = Sad Loss (you always lose)
• False weight formula: ERROR over FALSE. The guy gave you false weight, blame false in denominator: (True - False) / False x 100
• Discount chain: first knock down MP using discount to get SP, then knock down SP using profit% to get CP. Always top to bottom: MP to SP to CP

• Agniveer papers repeat the false weight and dishonest dealer problem almost every year — know the direct formula cold, it saves 90 seconds
• Discount plus profit combined question is the most common multi-step type — practice finding SP from MP first, then CP from SP
• Questions are mostly calculation-based with numbers under 1000 — avoid long division by using fraction shortcuts like 20% = 1/5, 25% = 1/4
• If a question says 'finds profit on SP' instead of CP, the formula changes to Profit% on SP = Profit/SP x 100 — read the question carefully
• Expected time per question: 45-60 seconds. If a question takes more than 90 seconds, mark and move — come back later