Question : If 7 men working 7 hours a day for each of 7 days produce 7 units of work, then the units of work produced by 5 men working 5 hrs a day for each of 5 days is:
Option 1: $\frac{25}{343}$
Option 2: $\frac{125}{49}$
Option 3: $\frac{49}{125}$
Option 4: $\frac{343}{25}$
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Correct Answer: $\frac{125}{49}$
Solution : Units of work by a group of 7 men, $W_1=7$ Time taken by them, $D_1=7$ days Number of hours they worked in a day, $T_1=7$ hours Let units of work by a group of 5 men be $W_{2}$ Time taken by them, $D_2=5$ days Number of hours they worked in a day, $T_2=5$ hours We know that, $\frac{M_{1}D_{1}T_{1}}{W_{1}} = \frac{M_{2}D_{2}T_{2}}{W_{2}}$ ⇒ $\frac{7 \times 7 \times 7}{7} = \frac{5 \times 5 \times 5}{W_2}$ ⇒ $49 \times W_2 = 125$ ⇒ $W_{2} = \frac{125}{49}$ Hence, the correct answer is $\frac{125}{49}$.
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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 : If 7 people working 4 hours a day can complete a task in 14 days. The number of days taken by 12 people working 8 hours a day will be:
Option 1: $5 \frac{1}{8}$ days
Option 2: $8$ days
Option 3: $4 \frac{1}{12}$ days
Option 4: $7 \frac{1}{4}$ days
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
Question : Rama alone can do a work in 5 days working 4 hours a day. Seema alone can do the same work in 3 days working 10 hours a day. How many hours do they need to work together in a day to complete the same work in 6 days?
Option 1: 1 hour
Option 2: 3 hours
Option 3: 5 hours
Option 4: 2 hours
Question : If 50 boys can finish a work in 30 days by working 6 hours per day, then how many hours per day should 25 boys work to finish that work within 24 days?
Option 1: 18 hours
Option 2: 10 hours
Option 3: 12 hours
Option 4: 15 hours
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