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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