Crack Profit, Loss, and Discount Problems Easily

Now we'll explore advanced strategies and shortcuts for solving complex profit and loss problems quickly.The first key strategy relates cost price, marked price, discount, and profit. We can express this as: Cost Price multiplied by one plus profit percentage equals Marked Price multiplied by one minus discount percentage.A common trap in profit and loss problems is assuming that a percentage increase followed by the same percentage decrease returns to the original value. This is incorrect.The actual formula to calculate the final value is: Original value times one plus x over 100, times one minus x over 100.This simplifies to: Original value times one minus x squared over ten thousand.For example, if we start with 100 dollars and apply a 20 percent increase, we get 120 dollars. If we then apply a 20 percent decrease to that amount, we end up with 96 dollars, not the original 100. This represents a 4 percent net loss.When dealing with multiple transactions, it's more efficient to track the overall effect rather than calculating each intermediate step.For example, if an item undergoes a 5 percent profit, followed by a 3 percent loss, and then a 2 percent profit...Instead of calculating each step separately, we can determine the overall effect by multiplying the factors: 1.05 times 0.97 times 1.02, which equals 1.0389, indicating a net profit of 3.89 percent.Our final strategy involves a special formula for identical articles. When one article is sold at a profit of x percent and another identical article at a loss of x percent, there's always a net loss.For example, if we sell one article at a 20 percent profit and another identical article at a 20 percent loss...The net result is a 4 percent loss, which we can calculate using our formula: x squared divided by 100. In this case, 20 squared divided by 100 equals 4 percent.These advanced strategies and shortcuts can transform complex profit and loss problems into simple formulas, saving you valuable time during exams.