Question : 4 men and 7 women can do work in 8 days. 7 men and 4 women can do the same work in 5 days. Find the number of days in which 8 women can finish the work.
Option 1: 60 days
Option 2: 55 days
Option 3: 40 days
Option 4: 45 days
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Correct Answer: 55 days
Solution : 4 men and 7 women can do 1 unit of work in 8 days. $⇒4m + 7w = \frac{1}{8}$ ____(i) where $m$ and $w$ are the efficiencies of a man and 1 woman respectively. 7 men and 4 women can do 1 unit of work in 5 days $⇒7m + 4w = \frac{1}{5}$ ____(ii) Multiplying the first equation by 7 and the second equation by 4, $⇒28m + 49w = \frac{7}{8}$ ____(iii) $⇒28m + 16w = \frac{4}{5}$ ____(iv) Subtracting the above equation, $⇒33w = \frac{7}{8} - \frac{4}{5} = \frac{3}{40}$ $⇒w=\frac{1}{11×40}$ $⇒w=\frac{1}{440}$ The work done by 8 women in a day, $⇒8w=\frac{8}{440}=\frac{1}{55}$ So, the required days = 55 days. Hence, the correct answer is 55 days.
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Question : 3 men or 5 women can do a work in 57 days. In how many days can 9 men and 4 women do that same work?
Option 1: 16 days
Option 2: 18 days
Option 3: 14 days
Option 4: 15 days
Question : 4 men and 8 women complete a job in 10 days and 5 men and 24 women complete the same work in 4 days. In how many days will 1 man and 1 woman complete the same work?
Option 1: $63 \frac{1}{3}$ days
Option 2: $69 \frac{7}{9}$ days
Option 3: $67 \frac{1}{3}$ days
Option 4: $62 \frac{2}{9}$ days
Question : 10 women can do a piece of work in 6 days, 6 men can do the same work in 5 days, and 8 children can do it in 10 days. What is the ratio of the efficiency of a woman, a man, and a child, respectively?
Option 1: 4 : 6 : 3
Option 2: 4 : 5 : 3
Option 3: 2 : 4 : 3
Option 4: 4 : 8 : 3
Question : 12 men can do work in 8 days while 4 boys can do it in 40 days. In how many days 9 boys and 3 men together will complete the same work?
Option 1: 10 days
Option 2: $\frac{280}{13}$ days
Option 3: $\frac{80}{7}$ days
Option 4: $\frac{260}{17}$ days
Question : A can finish a work in 25 days, and B can do the same work in 15 days. B worked for 10 days and left the job. A alone can finish the remaining work in how many days?
Option 1: $7 \frac{1}{3}$ days
Option 2: $6 \frac{1}{3}$ days
Option 3: $8 \frac{1}{3}$ days
Option 4: $5 \frac{1}{3}$ days
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