If ₹ 2800 is $\frac{2}{7}$ percent of the value of a house, the worth of the house (in ₹) is

### Concept & Formula This problem requires finding the total base value when a fractional percentage of it is known. The critical step is remembering that the percentage sign (%) means dividing the fraction itself by an additional 100. $$ \text{Value} = \left( \frac{\text{Fractional Percentage}}{100} \right) \times \text{Base} $$ ### Step-by-Step Solution * **Given:** Part value = ₹ 2800 Percentage = $ \frac{2}{7}\% $ * **Calculation:** Step 1: Set up the equation where $V$ is the total worth of the house. $ \left( \frac{2}{7}\% \right) \text{ of } V = 2800 $ Step 2: Convert the percentage into a proper numerical fraction by dividing by 100. $ \left( \frac{\frac{2}{7}}{100} \right) \times V = 2800 $ $ \left( \frac{2}{700} \right) \times V = 2800 $ Step 3: Isolate $V$ and solve. $ V = 2800 \times \left( \frac{700}{2} \right) $ $ V = 1400 \times 700 $ Step 4: Multiply out the final result. $ 14 \times 7 = 98 $ Append the four zeros: $ 980000 $ $ V = 9,80,000 $ ### Exam Strategy & Shortcut Think in terms of 1%. If $ \frac{2}{7}\% = 2800 $, you can find what $ \frac{1}{7}\% $ is by halving both sides. $ \frac{1}{7}\% = 1400 $. Now find 1% by multiplying both sides by 7. $ 1\% = 1400 \times 7 = 9800 $. If 1% of the house is 9800, then the total 100% value is simply 9800 with two more zeros added to the end. $ 100\% = 9,80,000 $. This completely avoids complex fraction-over-fraction algebra. ### Common Pitfall The most frequent error on this specific question type is ignoring the word "percent". Students will set up the equation as $ \frac{2}{7} \times V = 2800 $ (treating it as two-sevenths of the house, rather than two-sevenths of one percent). This will result in an incorrect answer of 9800, leaving them confused when looking at the options. Always divide by 100 when the "%" symbol is present. ### Final Answer **Therefore, the correct answer is 9,80,000.**