In a year, a man manages to sell only $65\%$ of the chicken he owns. How many chicken should the man own to sell $47775$ chicken in a year?

### Concept & Formula This problem involves finding the base value when a certain percentage of it is known. The governing formula is: $$\text{Percentage} \times \text{Total} = \text{Given Value}$$ ### Step-by-Step Solution **Given:** * Percentage of chickens sold = $65\%$ * Number of chickens sold = $47775$ **Calculation:** * Let the total number of chickens he owns be $x$. * According to the problem: $$65\% \text{ of } x = 47775$$ * Convert the percentage to a decimal or fraction: $$\frac{65}{100} \times x = 47775$$ * Isolate $x$: $$x = \frac{47775 \times 100}{65}$$ * Simplify the fraction by dividing by $5$ first: $$x = \frac{47775 \times 20}{13}$$ * Divide $47775$ by $13$: $$47775 \div 13 = 3675$$ * Multiply to find the final total: $$x = 3675 \times 20 = 73500$$ ### Exam Strategy & Shortcut If you are pressed for time, use approximation and unit digits. $65\%$ is roughly two-thirds ($\approx 66.6\%$). If two-thirds of the flock is $\sim 48000$, the whole flock is roughly $48000 \times 1.5 = 72000$. Looking at the options, $73000$ is close, but let's check the exact unit digit. $47775 \div 65$ means the multiplier must end in $5$ (since $5 \times 5 = 25$). So the answer must contain a $5$, giving $73500$ with the two zeros. Since $73500$ is not among the numeric options, you can confidently select "None of these". ### Common Pitfall Many students calculate the correct answer ($73500$), see $73000$ in the options, and assume they made a small rounding error, marking option (c). In banking and aptitude exams, "None of these" is frequently the correct answer and requires absolute confidence in your calculation. ### Final Answer **Therefore, the correct answer is None of these.**