Explanations:When dealing with successive discounts, it is important to understand that the second discount is applied to the price after the first discount has been applied. This means that the effective discount is not simply the sum of the individual discounts, but rather the result of applying each discount successively.
Let's consider an example to illustrate this concept. Suppose the original price of an article is \( P \). The first discount is 30%, so the price after the first discount is \( P \times (1 - 0.30) = P \times 0.70 \). The second discount is 40%, so the price after the second discount is \( P \times 0.70 \times (1 - 0.40) = P \times 0.70 \times 0.60 \).
Now, let's calculate the effective discount. The final price after both discounts is \( P \times 0.70 \times 0.60 = P \times 0.42 \). This means that the final price is 42% of the original price, so the effective discount is \( 100\% - 42\% = 58\% \).
The key concept here is that the second discount is applied to the reduced price after the first discount, not to the original price. This is why the effective discount is not simply the sum of the individual discounts (30% + 40% = 70%), but rather the result of applying each discount successively.
It is also important to note that the order of the discounts does not affect the final price. Whether the first discount is 30% and the second is 40%, or the first discount is 40% and the second is 30%, the final price will still be 42% of the original price, and the effective discount will still be 58%.
Understanding this concept is crucial for solving problems involving successive discounts, which are common in competitive exams such as CAT, MAT, Bank PO, and SSC.