Question : 10 women took 16 days to complete a work which can be completed by 6 men in 8 days. 12 men started working and after 2 days 6 men left and 5 women joined them. In how many days will the remaining work be completed?
Option 1: $\frac{3}{2}$
Option 2: $\frac{16}{5}$
Option 3: $\frac{5}{2}$
Option 4: $\frac{24}{5}$
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Correct Answer: $\frac{16}{5}$
Solution : Time taken by 10 women to complete the work = 16 days Time taken by 6 men to complete the work = 8 days Number of men working initially = 12 Number of men who left after 2 days = 6 Number of women who joined after 2 days = 5 Now, 10 women × 16 = 6 men × 8 1 woman=$\frac{3}{10}$ man Total work = 6 men × 8 days = 48 units (considering efficiency of 1 man is 1 unit) Work done by 12 men in 2 days= 12 × 2 = 24 Units Work left after 2 days = 48 − 24 = 24 units Number of men equivalents left = (6 + 5 × $\frac{3}{10}$) men= $\frac{15}2$ men So, $\frac{15}2$ men will do 24 units in = $\frac{48}{15} = \frac{16}5$ days Hence, the correct answer is $\frac{16}5$.
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