Question : If 90 men can do a certain job in 16 days, working 12 hours per day, then the part of that work which can be completed by 70 men in 24 days, working 8 hours per day is:
Option 1: $\frac{1}{3}$
Option 2: $\frac{2}{3}$
Option 3: $\frac{7}{9}$
Option 4: $\frac{5}{8}$
Correct Answer: $\frac{7}{9}$
Solution :
According to the question:
$\frac{M_1×D_1×T_1}{W_1}=\frac{M_2×D_2×T_2}{W_2}$ Where $M_1$ and $M_2$ are men, $D_1$ and $D_2$ are days and $W_1$ and $W_2$, are work done. $T_1$ and $T_2$ are hours per day.
So, $\frac{90×16×12}{1}=\frac{70×24×8}{W_2}$
⇒ $W_2=\frac{7}{9}$
Hence, the correct answer is $\frac{7}{9}$.
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