UPSKILL MATH PLUS

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Learn more**1. Overhead Expenses:**

Consider a situation that you're going to shop with your father to buy articles like machinery, furniture, electronic items, etc. These products are bought with some expenses on repairs, transportation and labour charges. These expenses are included in the Cost price and which is called as Overhead expenses.

Therefore, Total cost price \(=\) Cost price \(+\) Overhead expenses

**2. Successive Discounts:**

- In the case of Successive Discounts, the second discount is calculated on the reduced price after deducting the first discount from the marked price.
- Similarly, the third discount is calculated on the reduced price after deducting the second discounts and so on.

Important!

- If there are \(2\) successive discounts of \(a\%\) and \(b\%\) respectively, then: \(S.P\) \(=\) \((1-\frac{a}{100})(1-\frac{b}{100})\times M.P.\)
- Single discount equivalent to \(3\) successive discounts \(a\%\), \(b\%\) and \(c\%\) respectively \(=\) \(\{1-(1-\frac{a}{100})(1-\frac{b}{100})(1-\frac{c}{100})\}\)

Example:

Consider that you're going to buy a book for \(₹100\) with successive discounts of \(5\%\) and \(10\%\). Therefore the shop keeper first discount \(5\%\) of the total amount, which is as follows.

Here \(a\%\) \(=\) \(5\%\) and \(b\%\) \(=\) \(10\%\).

\(S.P\) \(=\) \((1-\frac{a}{100})(1-\frac{b}{100})\times M.P.\)

\(S.P\) \(=\) \((1-\frac{5}{100})(1-\frac{10}{100})\times 100\)

\(S.P\) \(=\) \((\frac{95}{100})(\frac{90}{100})\times 100\)

\(S.P\) \(=\) \(\frac{95 \times 90}{100}\)

\(S.P\) \(=\) \(85.5\)

Let us try the same problem by usual successive discounts.

\(=\) Total price \(\times\) \(5\%\)

\(=\) \(100 \times \frac{5}{100}\) \(=5\)

The reduced price \(=\) \(100-5\) \(₹95\)

Then this book also has a second discount of \(10\%\). So now we have to do the percentage calculation with the amount which is reduced from the first discount, which is as follows.

\(=\) Reduced price by first discount \(×\) \(10\%\)

$=95\phantom{\rule{0.147em}{0ex}}\times \frac{10}{100}\phantom{\rule{0.147em}{0ex}}=9.5$

The final price of the book after two successive discounts \(=\) \(95\) \(–\) \(9.5\) \(= ₹\)\(85.5\)