If 9 men working $${\text{7}}\frac{1}{2}$$ hours a day can finish a piece of work in 20 days, then how many days will be taken by 12 men, working 6 hours a day to finish the work ? (It is being given that 2 men of latter type work as much as 3 men of the former type.)
Correct Answer: $${\text{12}}\frac{1}{2}$$
Let the required number of days be x
2 men of latter type = 3 men of former type
12 men of latter type
= $$\left( {\frac{3}{2} \times 12} \right)$$
= 18 men of former type
More men, Less days (Indirect proportion)
Less working hours, More days (Indirect proportion)
\
$$\eqalign{ & \therefore \,18 \times 6 \times x = 9 \times \frac{{15}}{2} \times 20 \cr & \Leftrightarrow 108x = 1350 \cr & \Leftrightarrow x = \frac{{25}}{2} \cr & \Leftrightarrow x = 12\frac{1}{2} \cr} $$
2 men of latter type = 3 men of former type
12 men of latter type
= $$\left( {\frac{3}{2} \times 12} \right)$$
= 18 men of former type
More men, Less days (Indirect proportion)
Less working hours, More days (Indirect proportion)
\
$$\eqalign{ & \therefore \,18 \times 6 \times x = 9 \times \frac{{15}}{2} \times 20 \cr & \Leftrightarrow 108x = 1350 \cr & \Leftrightarrow x = \frac{{25}}{2} \cr & \Leftrightarrow x = 12\frac{1}{2} \cr} $$