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1. If 17 labourers can dig a ditch 26 m long in 18 days, working 8 hours a day; how many more labourers should be engaged to dig a similar ditch 39 m long in 6 days, each labourer working 9 hours a day ?

A. 34

B. 51

C. 68

D. 85

Solution:

Let the total number of men to be engaged be

x

More length, More labourers (Direct proportion)
Less days, More labourers (Indirect proportion)

\begin{matrix} Lentgh 26 : 39 \\ Days 6 : 18 \\ Hours per day 9 : 8 \end{matrix}} :: 17 : x

\begin{aligned} ∴ 26 \times 6 \times 9 \times x = 39 \times 18 \times 8 \times 17 \\ \Leftrightarrow x = \frac{(39 \times 18 \times 8 \times 17)}{(26 \times 6 \times 9)} \\ \Leftrightarrow x = 68 \end{aligned}

∴ Number of more labourers = (68 -17) = 51

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