The following table gives the income distribution of 200 households of a village: | Monthly Income (in ₹) | Number of Households | | :--- | :---: | | < 1000 | 25 | | < 2000 | 80 | | < 5000 | 170 | | < 10000 | 200 | What is the percentage of households whose monthly income is above ₹ 2000 but below ₹ 5000?

### Concept & Logic This problem requires interpreting a **Cumulative Frequency Distribution** table. The table gives the cumulative number of households earning "less than" a certain amount. To find the number of households in a specific range, we subtract the lower boundary's cumulative frequency from the upper boundary's cumulative frequency. $$ \text{Required Percentage} = \left( \frac{\text{Households in Range}}{\text{Total Households}} \right) \times 100 $$ ### Step-by-Step Solution * **Given**: * Total households = 200 * Households earning < ₹ 5000 = 170 * Households earning < ₹ 2000 = 80 * **Deduction**: * The number of households earning between ₹ 2000 and ₹ 5000 is the difference between these two cumulative values. * Households in range = $170 - 80 = 90$ * **Calculation**: * Percentage = $\left( \frac{90}{200} \right) \times 100$ * Percentage = $\frac{90}{2} = 45\%$ ### Exam Strategy & Shortcut Simply read the required range values directly from the table, subtract them mentally ($170 - 80 = 90$), and recognize that 90 out of 200 is exactly half of 90 out of 100. Thus, $\frac{90}{2} = 45$. This avoids writing down any intermediate steps. ### Common Pitfall A major mistake is using just one row of the table (e.g., using 170 and calculating $\frac{170}{200} = 85\%$). Always remember that "< 5000" includes the households already counted in "< 2000". You must subtract to find the specific class interval. ### Final Answer **Therefore, the correct answer is 45.**