Profit LossProfit Loss

Understanding foundational terms such as Cost Price (CP), Selling Price (SP), Marked Price (MP), Profit, and Loss is mandatory for solving basic arithmetic problems.

• Cost Price (CP): The price at which an article is purchased. Total CP includes additional overhead expenses like transportation, repair, and taxes.
• Selling Price (SP): The price at which an article is sold to the consumer or end-user.
• Profit and Loss Calculations: Profit = SP - CP (when SP > CP). Loss = CP - SP (when CP > SP). Both profit percentage and loss percentage are always calculated on the Cost Price unless specified otherwise.
• Marked Price & Discount: Marked Price (MP) is the labeled price. Discount is the reduction offered on MP. Discount = MP - SP, and Discount % = (Discount / MP) * 100.

Examiners frequently test concepts involving fraudulent practices such as using faulty weights or claiming to sell goods at cost price while generating hidden profits.

• False Weight Formula: When a dealer sells goods at cost price using a false weight, True Profit% = [(True Weight - False Weight) / False Weight] * 100.
• Combined Profit and False Weight: If a dealer promises a profit of x% on CP and also uses a false weight of y grams instead of 1000 grams, Overall Gain% = [{(100 + x) * (1000 / y)} - 100]%.
• Successive Discount Equivalents: Two successive discounts of a% and b% are equivalent to a single net discount of [a + b - (ab / 100)]%.
• Equal Percentage Profit and Loss on SP: If two articles are sold at the same selling price, one at a profit of x% and another at a loss of x%, there is always a net loss given by Loss% = (x / 10)^2.

Time-saving short tricks using fraction equivalents of percentages are vital for clearing the AHC RO/ARO preliminary and mains examinations within the stipulated time.

• Fractional Equivalents: Memorizing standard fractions like 1/8 = 12.5%, 1/6 = 16.67%, and 1/7 = 14.28% accelerates calculation speed for complex profit percentage problems.
• CP to SP Ratio Method: If profit is 16.67% (1/6), then CP:SP = 6:7. If loss is 12.5% (1/8), then CP:SP = 8:7. This enables direct proportional scaling.
• Marked Price to Cost Price Ratio: Direct relation between MP and CP given Discount% (D) and Profit% (P): MP / CP = (100 + P) / (100 - D).

Analysis of past Allahabad High Court RO/ARO and UPPSC exams reveals specific recurring patterns in numerical aptitude questions.

• Based on Quantity of Articles: If the Cost Price of 'x' articles equals the Selling Price of 'y' articles, Profit/Loss % = [(x - y) / y] * 100.
• Two Successive Sales (Chain Transactions): When A sells an article to B at a profit of x%, and B sells to C at a profit of y%, final effective price for C = CP_A * [(100+x)/100] * [(100+y)/100].
• Fluctuation in SP and CP: Problems where both CP and SP are changed by fixed amounts or percentages require equating initial and final profit equations to solve for original CP.