The price of an article is raised by 30% and then two successive discounts of 10% each are allowed. Ultimately, the price of the article is

### Concept & Successive Multipliers The most efficient way to track a series of percentage increases and decreases is to chain their decimal multipliers. A percentage increase of $r\%$ has a multiplier of $\left(1 + \frac{r}{100}\right)$, and a decrease has a multiplier of $\left(1 - \frac{r}{100}\right)$. $$Final = Initial \times M_1 \times M_2 \times M_3$$ ### Step-by-Step Solution * **Set Initial Base:** Let the initial price of the article be $100$. * **Apply the Increase:** * Raised by $30\%$. * Multiplier = $1.30$. * Price after increase = $100 \times 1.30 = 130$. * **Apply the First Discount:** * Discount of $10\%$. * Multiplier = $0.90$. * Price after 1st discount = $130 \times 0.90 = 117$. * **Apply the Second Discount:** * Discount of $10\%$. * Multiplier = $0.90$. * Final Price = $117 \times 0.90 = 105.3$. * **Determine Net Change:** * The price went from $100$ to $105.3$. * Net change = $105.3 - 100 = +5.3$. * This is an increase of $5.3\%$. ### Exam Strategy & Shortcut Skip the baseline $100$ and just multiply the factors: $$Net Multiplier = 1.3 \times 0.9 \times 0.9$$ $$Net Multiplier = 1.3 \times 0.81 = 1.053$$ $1.053$ is exactly $5.3\%$ above $1.000$, indicating a $5.3\%$ increase. This is extremely fast to calculate mentally or on scratch paper. ### Common Pitfall A frequent error is adding up the percentages directly ($+30\% - 10\% - 10\% = +10\%$ increase). Percentage changes are strictly multiplicative, never additive, because the base value changes with every step. ### Final Answer Therefore, the correct answer is **increased by 5.3%**.