10% of the inhabitants of a village having died of cholera, a panic set in, during which 25% of the remaining inhabitants left the village. The population is then reduced to 4050. Find the number of original inhabitants.
Answer
Answer (as printed):
Explanation
Let the total number of original inhabitants be $x$. Then, $(100-25)\%$ of $(100-10)\%$ of $x=4050 \Leftrightarrow \left(\frac{75}{100}\times\frac{90}{100}\times x\right)=4050 \Leftrightarrow \frac{27}{40}x=4050 \Leftrightarrow x=\left(\frac{4050\times 40}{27}\right)=6000$. Number of original inhabitants $=6000$.
Explanation as extracted from the printed page; notation may be imperfect.