15 persons working 8 hours a day can complete a work in 21 days. How many days will 14 persons take to complete a work $1 \frac{1}{2}$ times as great, if they work 6 hours a day? (S.S.C., 2006)
Answer
Answer (as printed):
Explanation
Let the required number of days be $x$. Less persons, More days (Indirect Proportion). Less hours per day, More days (Indirect Proportion). More work, More days (Direct Proportion). Persons $14:15$, Hours per day $6:8$, Work $\frac{3}{2}y : y$ :: $21:x$. $\therefore 14 \times 6 \times y \times x = 15 \times 8 \times \frac{3}{2} y \times 21 \Leftrightarrow x = \frac{15 \times 8 \times 3 y \times 21}{2 \times 14 \times 6 \times y} = 45$. Hence, required number of days $=45$.
Explanation as extracted from the printed page; notation may be imperfect.