The work done by a woman in 8 hours is equal to the work done by a man in 6 hours and by a boy in 12 hours. If working 6 hours per day 9 men can complete a work in 6 days, then in how many days can 12 men, 12 women and 12 boys together finish the same work, working 8 hours per day?
(a)$1 \frac{1}{2}$ days
(b)3 days
(c)$3 \frac{2}{3}$ days
(d)$4 \frac{1}{2}$ days
Answer
Answer (as printed): A
Explanation
Ratio of time taken by a woman, a man and a boy $= 8:6:12 = 4:3:6$. So, 4 women $\equiv$ 3 men $\equiv$ 6 boys. $(12 \text{ men} + 12 \text{ women} + 12 \text{ boys}) = \left(12 + \frac{3}{4} \times 12 + \frac{3}{6} \times 12\right)$ men $= (12+9+6)$ men $= 27$ men. Let the required number of days be $x$. More men, Less days (Indirect Proportion). More working hours, Less days (Indirect Proportion). Men $27:9$, Working hrs $8:6$ :: $6:x$. $\therefore 27 \times 8 \times x = 9 \times 6 \times 6 \Leftrightarrow x = \frac{9 \times 6 \times 6}{27 \times 8} = 1\frac{1}{2}$.
Explanation as extracted from the printed page; notation may be imperfect.