In profit and loss calculations, what is the fundamental relationship between cost price (CP), selling price (SP), and profit/loss percentage?
Answer
Profit or Loss % = ((SP - CP) / CP) * 100. A positive result indicates profit, a negative result indicates loss.
Question
What is the difference between a discount and a loss in profit and loss problems?
Answer
A discount is a reduction from the marked price (MP) to attract customers. A loss occurs when the selling price (SP) is less than the cost price (CP). They are calculated on different bases.
Question
If an item's cost price is CP and the desired profit percentage is P%, what is the formula to calculate the selling price (SP) without any discount?
Answer
SP = CP * (1 + P/100). For example, a 20% profit on CP 100 gives SP = 100 * 1.20 = 120.
Question
How do you calculate the marked price (MP) if you know the cost price (CP) and the desired profit percentage, before applying any discount?
Answer
If no discount is planned, MP is set equal to the desired selling price: MP = CP * (1 + Profit%/100). The MP is the price before any customer discount.
Question
An article is sold after a discount of d% on the marked price (MP). What is the key equation relating cost price (CP), selling price (SP), profit/loss, and discount?
Answer
SP = MP * (1 - d/100). Profit/Loss % is calculated on CP: ((SP - CP) / CP) * 100. The discount is applied to MP, not CP.
Question
In faulty weight problems, a seller uses a scale that shows 900g for every 1kg. If he sells at cost price, what is his effective profit percentage?
Answer
He gains by selling less quantity. Profit% = ((True Weight - False Weight) / False Weight) * 100 = ((1000 - 900) / 900) * 100 ≈ 11.11%.
Question
Two items are sold at the same selling price (SP), one at a profit of x% and the other at a loss of x%. What is the overall outcome?
Answer
There is always an overall net loss. The loss percentage is given by (x^2 / 100)%, regardless of the individual selling price.
Question
An item is bought and sold twice. For the first transaction, CP1 = 100, sold at 20% profit. For the second, it is bought again and sold at 10% loss. How do you find the overall profit/loss?
What is a key strategy for solving CAT problems where you need to find CP when SP and profit/loss % are given after a discount?
Answer
Assume a convenient value for CP (like 100). Work step-by-step: calculate MP from the desired profit, apply the given discount to find SP, and then scale to match the actual SP given.
Question
When comparing a single flat discount versus two successive discounts, how can you determine which gives a lower final price?
Answer
Calculate the net effective discount for successive discounts using: Net % = a + b - (a*b/100). Compare this to the flat discount. The scheme with the higher effective discount gives the lower final price.
Question
For Data Sufficiency questions in profit/loss, what is generally needed to find the profit percentage?
Answer
You need a relationship between at least two of the key variables: CP, SP, MP, or discount percentage. Often, two statements connecting these variables are required to find a unique solution.
Question
What is a key mental math shortcut for calculating the net effect of two successive discounts, a% and b%?
Answer
Calculate a + b - (a*b/100). For example, 20% and 10% gives 20 + 10 - (20*10/100) = 30 - 2 = 28% net discount.
Question
According to CAT time strategy, when should you consider skipping a profit and loss problem?
Answer
Skip lengthy word problems with multiple successive transactions, partnerships, or complex faulty weight problems if they involve many steps, unless you are very comfortable with the concepts.
Question
Why is it useful to memorize common percentage-to-fraction equivalents for CAT profit and loss problems?
Answer
It speeds up mental calculations. For example, 25% = 1/4, so a 25% profit on CP 100 means SP = 100 + (1/4)*100 = 125, which is faster than calculating 100 * 1.25.
