Question : If 4 men or 6 women can do a piece of work in 12 days, working 7 hours a day. How many days will it take to complete a work twice as large, with 10 men and 3 women working together 8 hours a day?
Option 1: 6 days
Option 2: 7 days
Option 3: 8 days
Option 4: 10 days
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Correct Answer: 7 days
Solution :
Given: 4 men or 6 women can do a piece of work in 12 days, working 7 hours a day.
4 men = 6 women, i.e. 2 men = 3 women
So, 10 men and 3 women = 10 + 2 = 12 men
Let 10 men and 3 women take D days to complete the work.
$\frac{M_1 ×D_1× h_1}{W_1}=\frac{M_2 ×D_2 × h_2}{W_2}$, where $M_1$ and $M_2$ are the numbers of men, and $D_1$ and $D_2$ are days, and $W_1$ and $W_2$ are work done, and $h_1$ and $h_2$ are working hours per day.
Now, according to the question,
$\frac{M_1 ×D_1× h_1}{W_1}=\frac{M_2 ×D_2 × h_2}{W_2}$
⇒ $\frac{4 ×12 × 7}{1}= \frac{12 ×D × 8}{2}$
⇒ D = 7 days
Hence, the correct answer is 7 days.
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