Question : 16 women take 12 days to complete a work which can be completed by 12 men in 8 days. 16 men started working and after 3 days 10 men left and 4 women joined them. How many days will it take them to complete the remaining work?
Option 1: 4
Option 2: 6
Option 3: 8
Option 4: 10
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Correct Answer: 6
Solution :
Work done by 12 men in 8 days = Work done by 16 women in 12 days
⇒ 12 × 8 men = 16 × 12 women
⇒ 1 man = 2 women
Now, work done by 12 men in 1 day = $\frac{1}{8}$
Work done by 1 man in 1 day = $\frac{1}{12×8}=\frac{1}{96}$
Work done by 16 men in 3 days = $\frac{16×1×3}{96}=\frac{1}{2}$
Remaining work = $1-\frac{1}{2}=\frac{1}{2}$
Remaining work is be done by 6 men + 4 women = 6 men + 2 men = 8 men
Work done by 8 men in a day = $\frac{1}{96}\times 8=\frac{1}{12}$
$\therefore$ Time taken to do remaining work = $\frac{\text{Work left}}{\text{Work done by 8 men in a day}}$
= $\frac{\frac{1}{2}}{\frac{1}{12}}$
= 6 days
Hence, the correct answer is 6.
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