5 press compositors can set 625 pages of a manuscript in 16 days of $10\frac{1}{2}$ hours each. Each page has 60 lines and each line has 40 letters. In how many days of 8 hours each, will 10 compositors set 1000 pages of a manuscript, each page having 45 lines with 50 letters in each line?
Answer
Answer (as printed):
Explanation
Let the required number of days be $x$. More compositors, Less days (Indirect Proportion). More pages, More days (Direct Proportion). Less hours per day, More days (Indirect Proportion). Less lines per page, Less days (Direct Proportion). More letters per line, More days (Direct Proportion). Compositors $10:5$, Pages $625:1000$, Hours per day $8:\frac{21}{2}$, Lines per page $60:45$, Letters per line $40:50$, all $::16:x$. $$\therefore 10\times625\times8\times60\times40\times x=5\times1000\times\frac{21}{2}\times45\times50\times16$$ $$\Rightarrow x=\frac{5\times1000\times21\times45\times50\times16}{2\times10\times625\times8\times60\times40}=\frac{63}{4}=15\frac{3}{4}.$$ Hence, required number of days $=15\frac{3}{4}$.
Explanation as extracted from the printed page; notation may be imperfect.