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
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Correct Answer: $\frac{80}{7}$ days
Solution : 12 men can do work in 8 days while 4 boys can do it in 40 days. $M_{1}D_{1} = M_{2}D_{2}$ $⇒ 12 \text{ men} \times 8 = 4 \text{ boys} \times 40$ $⇒ 12 \text{ men} = 4 \text{ boys} \times\frac{40}{8}$ $⇒ 3 \text{ men} = 5 \text{ boys}$ $⇒ 1 \text{ man} = \frac{5}{3} \text{ boys}$ Now in the second case, 4 boys can do work in 40 days. 1 boy can do the work in 40 × 4 days = 160 days 9 boys and 3 men = $9 + \frac{5}{3} \times 3$ boys 9 boys and 3 men = 14 boys 14 boys can do in = $\frac{160}{14} = \frac{80}{7}$ days. Hence, the correct answer is $\frac{80}{7}$ days.
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Question : If a man completed a work in 10 days and the same work was completed by a woman in 8 days. How many days will it take to complete if they work together?
Option 1: $\frac{38}{8}$
Option 2: $\frac{40}{7}$
Option 3: $\frac{40}{9}$
Option 4: $\frac{42}{9}$
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 : 30 women working 5 hours a day can complete a work in 18 days, In how many days will 21 women working 8 hours a day complete the same work?
Option 1: $18 \frac{7}{13}$ days
Option 2: $17 \frac{11}{13}$ days
Option 3: $16 \frac{1}{14}$ days
Option 4: $13 \frac{3}{14}$ days
Question : A can do 75% of a job in 9 days and B can do half of the job in 8 days. If they work on it together then in how many days can they do half of the job?
Option 1: $\frac{40}{7}$
Option 2: $\frac{24}{7}$
Option 3: $\frac{7}{2}$
Option 4: $\frac{9}{2}$
Question : A can do a certain work in 9 days. B is 80% more efficient than A. How many days will B and A together take to do the same work?
Option 1: $\frac{45}{14}$ Days
Option 2: $\frac{54}{13}$ Days
Option 3: $\frac{47}{14}$ Days
Option 4: $\frac{44}{13}$ Days
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