The price of an article was first increased by 10% and then again by 20%. If the last increased price be ₹ 33, the original price was

Concept & Formula This problem requires working backward to find an initial base value after successive percentage changes. We can use the effective percentage change formula to find the total combined increase, and then map it mathematically to the given final price. $$Net Change = a + b + \frac{a \times b}{100}$$ Step-by-Step Solution * **Given:** First increase $a = 10\%$, second increase $b = 20\%$. Final price = 33. * **Calculation:** First, calculate the equivalent single percentage increase: $$Net Change = 10 + 20 + \frac{10 \times 20}{100}$$ $$Net Change = 30 + \frac{200}{100} = 32\%$$ Let the original price of the article be $x$. After a 32% increase, the new price is 132% of $x$. $$1.32 \times x = 33$$ $$x = \frac{33}{1.32}$$ $$x = \frac{3300}{132}$$ Dividing both the numerator and denominator by 33: $$x = \frac{100}{4} = 25$$ Exam Strategy & Shortcut Use the fraction/multiplier chain method to build a solvable equation in one quick line. A 10% increase multiplies the base by $\frac{11}{10}$. A 20% increase multiplies the base by $\frac{12}{10}$ (which simplifies to $\frac{6}{5}$). $$x \times \frac{11}{10} \times \frac{6}{5} = 33$$ $$x \times \frac{66}{50} = 33$$ $$x = \frac{33 \times 50}{66} = \frac{50}{2} = 25$$ This cleanly avoids decimal division entirely, saving crucial seconds. Common Pitfall Working backwards by blindly decreasing 33 by 20% and then by 10% will yield the wrong answer. Percentage increases and decreases are not perfectly reversible because the base changes at every step. Always set up the forward algebraic equation to solve for the unknown original value. Final Answer **Therefore, the correct answer is ₹ 25.**