Question : If 10 men can complete a piece of work in 12 days by working 7 hours a day, then in how many days can 14 men do the same work by working 6 hours a day?
Option 1: 15
Option 2: 16
Option 3: 10
Option 4: 12
Correct Answer: 10
Solution :
$\frac{M_1 D_1 H_1}{W_1} = \frac{M_2 D_2 H_2}{W_2}$
Where $M_1$ and $M_2$ are men, $H_1$ and $H_2$ are working hours per day, $D_1$ and $D_2$ are days, and $W_1$ and $W_2$ are work done
Given:
According to the question,
$ \frac{M_1 D_1 H_1}{W_1} = \frac{M_2 D_2 H_2}{W_2}$
$\Rightarrow \frac{10\times 12\times 7}{W} = \frac{14\times D_2\times 6}{W}$
$\Rightarrow D_2 =\frac{10\times 12\times 7}{14\times 6}$
$\therefore D_2 = 10$
Hence, the correct answer is 10.
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