64 persons can dig a trench 50 m long, 2 m wide and 2 m deep in 5 days, working 12 hours daily. In how many days, working 8 hours daily, will 80 persons dig another trench 75 m long, 4 m wide and 3 m deep?
(a)18
(b)27
(c)36
(d)45
Answer
Answer (as printed): B
Explanation
Let the required number of days be $x$. More persons, Less days (Indirect Proportion). More length, More days (Direct Proportion). More width, More days (Direct Proportion). More depth, More days (Direct Proportion). Less working hrs, More days (Indirect Proportion). Persons $80:64$, Length $50:75$, Width $2:4$, Depth $2:3$, Working hrs $8:12$ :: $5:x$. $\therefore 80 \times 50 \times 2 \times 2 \times 8 \times x = 64 \times 75 \times 4 \times 3 \times 12 \times 5 \Leftrightarrow x = \frac{64 \times 75 \times 4 \times 3 \times 12 \times 5}{80 \times 50 \times 2 \times 2 \times 8} = 27$.
Explanation as extracted from the printed page; notation may be imperfect.