Question
30 labourers working 7 hours a day can finish a piece of work in 18 days. If the labourers work 6 hours a day, then the number of labourers to finish the same piece of work in 30 days, will be ?
Answer: Option B
Let the required number of labourers be x
Less working hour/day, More labours (Indirect proportion)
More days, Less labourers (Indirect proportion)
\[\left. \begin{gathered}
{\text{Working hours/day 6}}:7 \hfill \\
\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,{\text{Days 30}}:18 \hfill \\
\end{gathered} \right\}::30:x\]
$$\eqalign{
& \therefore 6 \times 30 \times x = 7 \times 18 \times 30 \cr
& \Leftrightarrow 6x = 126 \cr
& \Leftrightarrow x = 21 \cr} $$
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Let the required number of labourers be x
Less working hour/day, More labours (Indirect proportion)
More days, Less labourers (Indirect proportion)
\[\left. \begin{gathered}
{\text{Working hours/day 6}}:7 \hfill \\
\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,{\text{Days 30}}:18 \hfill \\
\end{gathered} \right\}::30:x\]
$$\eqalign{
& \therefore 6 \times 30 \times x = 7 \times 18 \times 30 \cr
& \Leftrightarrow 6x = 126 \cr
& \Leftrightarrow x = 21 \cr} $$
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