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1. If 9 men working $7 \frac{1}{2}$ 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.)

A. $9 \frac{1}{2}$

B. 11

C. $12 \frac{1}{2}$

D. 13

Solution:

Let the required number of days be x
2 men of latter type = 3 men of former type
12 men of latter type
=

(\frac{3}{2} \times 12)

= 18 men of former type
More men, Less days (Indirect proportion)
Less working hours, More days (Indirect proportion)

\begin{matrix} Men 18 : 9 \\ Working hrs 6 : \frac{15}{2} \end{matrix}} :: 20 : x

\begin{aligned} ∴ 18 \times 6 \times x = 9 \times \frac{15}{2} \times 20 \\ \Leftrightarrow 108 x = 1350 \\ \Leftrightarrow x = \frac{25}{2} \\ \Leftrightarrow x = 12 \frac{1}{2} \end{aligned}

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