The cost price of an article is decreased by 10% and then increased by 20%. If the final price is ₹540, then the original cost price is:

​Decrease in cost price = 10%

Increase in cost price = 20%

Final price after changes = ₹540

If the cost price is first decreased by x% and then increased by y%, the final price $$P_f$$​ can be found using the original price$$P_o$$​​ as:

​$$P_f = P_o \times \left( 1 - \frac{x}{100} \right) \times \left( 1 + \frac{y}{100} \right)$$​​

where x is the percentage decrease and y is the percentage increase.

Let the original cost price be $$P_o​.$$​​

According to the question:

​$$\begin{aligned}&540 = P_o\times \left( 1 - \frac{10}{100} \right) \times \left( 1 + \frac{20}{100} \right) \\ &540 = P_o \times 0.9 \times 1.2 \\&540 = P_o \times 1.08 \\&P_o = \frac{540}{1.08} = 500\end{aligned}$$​​

Alternate Solution:  ​

using fraction; 10% = $$\frac{1}{10}$$​  and 20% = $$\frac{1}{5}$$ ​

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